Descriptive statistics are methods of describing the characteristics of a data set. It includes calculating things such as the average of the data, its spread and the shape it produces.
Descriptive statistics are used to describe and summarize the basic features of data through measures of central tendency like the mean, median, and mode, and measures of variability like range, variance and standard deviation. The mean is the average value and is best for continuous, non-skewed data. The median is less affected by outliers and is best for skewed or ordinal data. The mode is the most frequent value and is used for categorical data. Measures of variability describe how spread out the data is, with higher values indicating more dispersion.
This document discusses statistics and their uses in various fields such as business, health, learning, research, social sciences, and natural resources. It provides examples of how statistics are used in starting businesses, manufacturing, marketing, and engineering. Statistics help decision-makers reduce ambiguity and assess risks. They are used to interpret data and make informed decisions. However, statistics also have limitations as they only show averages and may not apply to individuals.
This document defines data and different types of data presentation. It discusses quantitative and qualitative data, and different scales for qualitative data. The document also covers different ways to present data scientifically, including through tables, graphs, charts and diagrams. Key types of visual presentation covered are bar charts, histograms, pie charts and line diagrams. Presentation should aim to clearly convey information in a concise and systematic manner.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
This presentation is about Basic Statistics-related to types of Data-Qualitative and Quantitative, and its Examples in everyday life- By: Dr. Farhana Shaheen
This document provides an overview of inferential statistics. It defines inferential statistics as using samples to draw conclusions about populations and make predictions. It discusses key concepts like hypothesis testing, null and alternative hypotheses, type I and type II errors, significance levels, power, and effect size. Common inferential tests like t-tests, ANOVA, and meta-analyses are also introduced. The document emphasizes that inferential statistics allow researchers to generalize from samples to populations and test hypotheses about relationships between variables.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
Descriptive statistics are used to describe and summarize the basic features of data through measures of central tendency like the mean, median, and mode, and measures of variability like range, variance and standard deviation. The mean is the average value and is best for continuous, non-skewed data. The median is less affected by outliers and is best for skewed or ordinal data. The mode is the most frequent value and is used for categorical data. Measures of variability describe how spread out the data is, with higher values indicating more dispersion.
This document discusses statistics and their uses in various fields such as business, health, learning, research, social sciences, and natural resources. It provides examples of how statistics are used in starting businesses, manufacturing, marketing, and engineering. Statistics help decision-makers reduce ambiguity and assess risks. They are used to interpret data and make informed decisions. However, statistics also have limitations as they only show averages and may not apply to individuals.
This document defines data and different types of data presentation. It discusses quantitative and qualitative data, and different scales for qualitative data. The document also covers different ways to present data scientifically, including through tables, graphs, charts and diagrams. Key types of visual presentation covered are bar charts, histograms, pie charts and line diagrams. Presentation should aim to clearly convey information in a concise and systematic manner.
This presentation includes an introduction to statistics, introduction to sampling methods, collection of data, classification and tabulation, frequency distribution, graphs and measures of central tendency.
This presentation is about Basic Statistics-related to types of Data-Qualitative and Quantitative, and its Examples in everyday life- By: Dr. Farhana Shaheen
This document provides an overview of inferential statistics. It defines inferential statistics as using samples to draw conclusions about populations and make predictions. It discusses key concepts like hypothesis testing, null and alternative hypotheses, type I and type II errors, significance levels, power, and effect size. Common inferential tests like t-tests, ANOVA, and meta-analyses are also introduced. The document emphasizes that inferential statistics allow researchers to generalize from samples to populations and test hypotheses about relationships between variables.
Analysis of data is a process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making.
This document discusses measures of central tendency, including the mean, median, and mode. It provides examples of calculating each measure using sample data sets. The mean is the average value calculated by summing all values and dividing by the number of data points. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequently occurring value. Examples are given to demonstrate calculating the mean, median, and mode from sets of numeric data.
This document discusses inferential statistics, which uses sample data to make inferences about populations. It explains that inferential statistics is based on probability and aims to determine if observed differences between groups are dependable or due to chance. The key purposes of inferential statistics are estimating population parameters from samples and testing hypotheses. It discusses important concepts like sampling distributions, confidence intervals, null hypotheses, levels of significance, type I and type II errors, and choosing appropriate statistical tests.
Basic statistics is the science of collecting, organizing, summarizing, and interpreting data. It allows researchers to gain insights from data through graphical or numerical summaries, regardless of the amount of data. Descriptive statistics can be used to describe single variables through frequencies, percentages, means, and standard deviations. Inferential statistics make inferences about phenomena through hypothesis testing, correlations, and predicting relationships between variables.
This document discusses descriptive statistics and how to calculate them. It covers preparing data for analysis through coding and tabulation. It then defines four types of descriptive statistics: measures of central tendency like mean, median, and mode; measures of variability like range and standard deviation; measures of relative position like percentiles and z-scores; and measures of relationships like correlation coefficients. It provides formulas for calculating common descriptive statistics like the mean, standard deviation, and Pearson correlation.
This document discusses multivariate analysis (MVA), which involves observing and analyzing multiple outcome variables simultaneously. It describes key components of MVA like variates, measurement scales, and statistical significance. Various MVA techniques are explained, including cross correlations, single-equation models, vector autoregressions, and cointegration. An example using crime rate data from US states is provided. Applications of MVA in fields like marketing, quality control, process optimization, and research are also mentioned.
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
RESEARCH METHODOLOGY- PROCESSING OF DATAjeni jerry
This document discusses research methodology and the processing of data. It outlines important steps in preparing raw data for analysis, including questionnaire checking, editing, coding, classification, tabulation, and graphical representation. The document also covers data cleaning and adjusting to ensure consistency and handle missing values, improving the quality of analysis. Proper data preparation through these steps is necessary to obtain reliable results from the analysis.
This document introduces the concept of data classification and levels of measurement in statistics. It explains that data can be either qualitative or quantitative. Qualitative data consists of attributes and labels while quantitative data involves numerical measurements. The document also outlines the four levels of measurement - nominal, ordinal, interval, and ratio - from lowest to highest. Each level allows for different types of statistical calculations, with the ratio level permitting the most complex calculations like ratios of two values.
This document provides an overview of key concepts in sampling and statistics. It defines population as the entire set of items from which a sample can be drawn. It discusses different types of sampling methods including probability sampling (simple random, stratified, cluster, systematic) and non-probability sampling (convenience, judgmental, quota, snowball). It also defines key terms like bias, precision, randomization. The document discusses the sampling process and compares advantages and disadvantages of sampling. It provides examples of calculating standard error of mean and proportion. Finally, it distinguishes between standard deviation and standard error.
Missing data occurs when no data value is stored for a variable in an observation, usually due to manual errors or incorrect measurements. There are three types of missing data: missing completely at random, missing at random, and missing not at random. Several methods can be used to deal with missing data, including reducing the dataset, treating missing values as a special value, replacing with the mean, replacing with the most common value, and using the closest fit to impute missing values. Proper handling of missing data is important to avoid bias and distortions in analyzing the data.
Statistics can be defined in both a singular and plural sense. In the singular sense, it refers to statistical methods for collecting, analyzing, and interpreting numerical data. In the plural sense, it refers to the actual numerical facts or data collected. Statistics involves systematically collecting, organizing, presenting, analyzing, and interpreting numerical data to describe features and characteristics. It allows for comparing facts, establishing relationships, and facilitating policymaking and decision making. However, statistics only studies aggregates and averages, not individual cases, and results are true only on average. It also requires properly contextualizing and referencing results.
1. The document discusses descriptive statistics, which is the study of how to collect, organize, analyze, and interpret numerical data.
2. Descriptive statistics can be used to describe data through measures of central tendency like the mean, median, and mode as well as measures of variability like the range.
3. These statistical techniques help summarize and communicate patterns in data in a concise manner.
This document discusses sampling and sampling distributions. It begins by explaining why sampling is preferable to a census in terms of time, cost and practicality. It then defines the sampling frame as the listing of items that make up the population. Different types of samples are described, including probability and non-probability samples. Probability samples include simple random, systematic, stratified, and cluster samples. Key aspects of each type are defined. The document also discusses sampling distributions and how the distribution of sample statistics such as means and proportions can be approximated as normal even if the population is not normal, due to the central limit theorem. It provides examples of how to calculate probabilities and intervals for sampling distributions.
Introduction to statistics...ppt rahulRahul Dhaker
This document provides an introduction to statistics and biostatistics. It discusses key concepts including:
- The definitions and origins of statistics and biostatistics. Biostatistics applies statistical methods to biological and medical data.
- The four main scales of measurement: nominal, ordinal, interval, and ratio scales. Nominal scales classify data into categories while ratio scales allow for comparisons of magnitudes and ratios.
- Descriptive statistics which organize and summarize data through methods like frequency distributions, measures of central tendency, and graphs. Frequency distributions condense data into tables and charts. Measures of central tendency include the mean, median, and mode.
This document provides an overview of sampling techniques. It defines key sampling terms like population, sample, sampling frame, and discusses the need for sampling due to constraints of time and money for a full census. The document outlines different sampling methods like simple random sampling, stratified sampling, cluster sampling and multistage sampling. It also discusses non-probability sampling techniques like convenience sampling and snowball sampling. The document emphasizes the importance of representativeness, adequacy and independence for a good sample. It concludes by noting sources of error in sampling like sampling errors and non-sampling errors.
- Sampling distribution describes the distribution of sample statistics like means or proportions drawn from a population. It allows making statistical inferences about the population.
- The central limit theorem states that sampling distributions of sample means will be approximately normally distributed regardless of the population distribution, if the sample size is large.
- Standard error measures the amount of variability in values of a sample statistic across different samples. It is used to construct confidence intervals for population parameters.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
Statistical Data Analysis | Data Analysis | Statistics Services | Data Collec...Stats Statswork
The present article helps the USA, the UK and the Australian students pursuing their business and marketing postgraduate degree to identify right topic in the area of marketing in business. These topics are researched in-depth at the University of Columbia, brandies, Coventry, Idaho, and many more. Stats work offers UK Dissertation stats work Topics Services in business. When you Order stats work Dissertation Services at Tutors India, we promise you the following – Plagiarism free, Always on Time, outstanding customer support, written to Standard, Unlimited Revisions support and High-quality Subject Matter Experts.
Contact Us:
Website: www.statswork.com
Email: info@statswork.com
UnitedKingdom: +44-1143520021
India: +91-4448137070
WhatsApp: +91-8754446690
This document contains tables and information about quantitative techniques including:
1) An area under the normal curve table that provides the proportion of the normal curve between values of z.
2) A binomial coefficients table that lists coefficients for values up to 20.
3) A table of values of the Poisson probability function for values of m from 0 to 9.
The document introduces the statistical concepts of mean, median, mode, and range using everyday examples like test scores and family ages. It explains that mean is the average, median is the middle number, mode is the most frequent value, and range is the difference between the highest and lowest numbers. Various examples are provided and explained step-by-step to illustrate how to calculate each statistical measure.
This document discusses measures of central tendency, including the mean, median, and mode. It provides examples of calculating each measure using sample data sets. The mean is the average value calculated by summing all values and dividing by the number of data points. The median is the middle value when data is ordered from lowest to highest. The mode is the most frequently occurring value. Examples are given to demonstrate calculating the mean, median, and mode from sets of numeric data.
This document discusses inferential statistics, which uses sample data to make inferences about populations. It explains that inferential statistics is based on probability and aims to determine if observed differences between groups are dependable or due to chance. The key purposes of inferential statistics are estimating population parameters from samples and testing hypotheses. It discusses important concepts like sampling distributions, confidence intervals, null hypotheses, levels of significance, type I and type II errors, and choosing appropriate statistical tests.
Basic statistics is the science of collecting, organizing, summarizing, and interpreting data. It allows researchers to gain insights from data through graphical or numerical summaries, regardless of the amount of data. Descriptive statistics can be used to describe single variables through frequencies, percentages, means, and standard deviations. Inferential statistics make inferences about phenomena through hypothesis testing, correlations, and predicting relationships between variables.
This document discusses descriptive statistics and how to calculate them. It covers preparing data for analysis through coding and tabulation. It then defines four types of descriptive statistics: measures of central tendency like mean, median, and mode; measures of variability like range and standard deviation; measures of relative position like percentiles and z-scores; and measures of relationships like correlation coefficients. It provides formulas for calculating common descriptive statistics like the mean, standard deviation, and Pearson correlation.
This document discusses multivariate analysis (MVA), which involves observing and analyzing multiple outcome variables simultaneously. It describes key components of MVA like variates, measurement scales, and statistical significance. Various MVA techniques are explained, including cross correlations, single-equation models, vector autoregressions, and cointegration. An example using crime rate data from US states is provided. Applications of MVA in fields like marketing, quality control, process optimization, and research are also mentioned.
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
RESEARCH METHODOLOGY- PROCESSING OF DATAjeni jerry
This document discusses research methodology and the processing of data. It outlines important steps in preparing raw data for analysis, including questionnaire checking, editing, coding, classification, tabulation, and graphical representation. The document also covers data cleaning and adjusting to ensure consistency and handle missing values, improving the quality of analysis. Proper data preparation through these steps is necessary to obtain reliable results from the analysis.
This document introduces the concept of data classification and levels of measurement in statistics. It explains that data can be either qualitative or quantitative. Qualitative data consists of attributes and labels while quantitative data involves numerical measurements. The document also outlines the four levels of measurement - nominal, ordinal, interval, and ratio - from lowest to highest. Each level allows for different types of statistical calculations, with the ratio level permitting the most complex calculations like ratios of two values.
This document provides an overview of key concepts in sampling and statistics. It defines population as the entire set of items from which a sample can be drawn. It discusses different types of sampling methods including probability sampling (simple random, stratified, cluster, systematic) and non-probability sampling (convenience, judgmental, quota, snowball). It also defines key terms like bias, precision, randomization. The document discusses the sampling process and compares advantages and disadvantages of sampling. It provides examples of calculating standard error of mean and proportion. Finally, it distinguishes between standard deviation and standard error.
Missing data occurs when no data value is stored for a variable in an observation, usually due to manual errors or incorrect measurements. There are three types of missing data: missing completely at random, missing at random, and missing not at random. Several methods can be used to deal with missing data, including reducing the dataset, treating missing values as a special value, replacing with the mean, replacing with the most common value, and using the closest fit to impute missing values. Proper handling of missing data is important to avoid bias and distortions in analyzing the data.
Statistics can be defined in both a singular and plural sense. In the singular sense, it refers to statistical methods for collecting, analyzing, and interpreting numerical data. In the plural sense, it refers to the actual numerical facts or data collected. Statistics involves systematically collecting, organizing, presenting, analyzing, and interpreting numerical data to describe features and characteristics. It allows for comparing facts, establishing relationships, and facilitating policymaking and decision making. However, statistics only studies aggregates and averages, not individual cases, and results are true only on average. It also requires properly contextualizing and referencing results.
1. The document discusses descriptive statistics, which is the study of how to collect, organize, analyze, and interpret numerical data.
2. Descriptive statistics can be used to describe data through measures of central tendency like the mean, median, and mode as well as measures of variability like the range.
3. These statistical techniques help summarize and communicate patterns in data in a concise manner.
This document discusses sampling and sampling distributions. It begins by explaining why sampling is preferable to a census in terms of time, cost and practicality. It then defines the sampling frame as the listing of items that make up the population. Different types of samples are described, including probability and non-probability samples. Probability samples include simple random, systematic, stratified, and cluster samples. Key aspects of each type are defined. The document also discusses sampling distributions and how the distribution of sample statistics such as means and proportions can be approximated as normal even if the population is not normal, due to the central limit theorem. It provides examples of how to calculate probabilities and intervals for sampling distributions.
Introduction to statistics...ppt rahulRahul Dhaker
This document provides an introduction to statistics and biostatistics. It discusses key concepts including:
- The definitions and origins of statistics and biostatistics. Biostatistics applies statistical methods to biological and medical data.
- The four main scales of measurement: nominal, ordinal, interval, and ratio scales. Nominal scales classify data into categories while ratio scales allow for comparisons of magnitudes and ratios.
- Descriptive statistics which organize and summarize data through methods like frequency distributions, measures of central tendency, and graphs. Frequency distributions condense data into tables and charts. Measures of central tendency include the mean, median, and mode.
This document provides an overview of sampling techniques. It defines key sampling terms like population, sample, sampling frame, and discusses the need for sampling due to constraints of time and money for a full census. The document outlines different sampling methods like simple random sampling, stratified sampling, cluster sampling and multistage sampling. It also discusses non-probability sampling techniques like convenience sampling and snowball sampling. The document emphasizes the importance of representativeness, adequacy and independence for a good sample. It concludes by noting sources of error in sampling like sampling errors and non-sampling errors.
- Sampling distribution describes the distribution of sample statistics like means or proportions drawn from a population. It allows making statistical inferences about the population.
- The central limit theorem states that sampling distributions of sample means will be approximately normally distributed regardless of the population distribution, if the sample size is large.
- Standard error measures the amount of variability in values of a sample statistic across different samples. It is used to construct confidence intervals for population parameters.
1. Statistics is used to analyze data beyond what can be seen in maps and diagrams by using mathematical manipulation, which can reveal patterns that may otherwise go unnoticed.
2. It is important to justify any statistical techniques used and to only use techniques that are appropriate for the type of data.
3. Common methods for summarizing large data sets include calculating the mean, mode, and median. The mean is the average, the mode is the most frequent value, and the median is the middle value when the data is arranged from lowest to highest.
Statistical Data Analysis | Data Analysis | Statistics Services | Data Collec...Stats Statswork
The present article helps the USA, the UK and the Australian students pursuing their business and marketing postgraduate degree to identify right topic in the area of marketing in business. These topics are researched in-depth at the University of Columbia, brandies, Coventry, Idaho, and many more. Stats work offers UK Dissertation stats work Topics Services in business. When you Order stats work Dissertation Services at Tutors India, we promise you the following – Plagiarism free, Always on Time, outstanding customer support, written to Standard, Unlimited Revisions support and High-quality Subject Matter Experts.
Contact Us:
Website: www.statswork.com
Email: info@statswork.com
UnitedKingdom: +44-1143520021
India: +91-4448137070
WhatsApp: +91-8754446690
This document contains tables and information about quantitative techniques including:
1) An area under the normal curve table that provides the proportion of the normal curve between values of z.
2) A binomial coefficients table that lists coefficients for values up to 20.
3) A table of values of the Poisson probability function for values of m from 0 to 9.
The document introduces the statistical concepts of mean, median, mode, and range using everyday examples like test scores and family ages. It explains that mean is the average, median is the middle number, mode is the most frequent value, and range is the difference between the highest and lowest numbers. Various examples are provided and explained step-by-step to illustrate how to calculate each statistical measure.
Reporting Statistics in Psychology
This document provides guidelines for reporting statistics in psychology research. It outlines how to round numbers and report means, standard deviations, p-values, effect sizes, and results from t-tests, ANOVAs, and other statistical analyses. Key recommendations include reporting exact p-values to two or three decimal places, using abbreviations like M and SD consistently, and noting any violations of statistical assumptions.
The Content Marketing Metrics That Matter (#CMWorld 2015)PR 20/20
Marketing technology advances have made it easier and more affordable to connect activities to outcomes, but content marketers have largely dropped the ball when it comes to monitoring, reporting and improving performance. The key is to align content marketing KPIs with overall business goals, have a logical and well-documented process for updating and reporting results, and develop systems for turning data into intelligence and intelligence into action.
Attendee takeaways:
* Prioritize content marketing goals.
* Identify Key Performance Indicators (KPIs).
* Select the right analytics technology and tools.
* Optimize your use of Google Analytics.
* Turn data into insights and actions.
This document provides an overview of big data, including definitions, characteristics, and technologies. It defines big data as large datasets that cannot be processed by traditional databases due to size and complexity. It describes the key aspects of big data as volume, variety, velocity, and veracity. The document also discusses how big data differs from traditional transaction systems, the promise and challenges of big data, and Hadoop as a framework for distributed processing of big data.
The document discusses developing an effective enterprise data strategy. It recommends that a data strategy should include identifying and combining multiple data sources, building advanced analytics models, and enabling organizational transformation. An effective strategy also makes data generate business value, identifies critical data assets, defines the data ecosystem, and establishes data governance. The strategy must be flexible, actionable, and provide a clear vision of how data and analytics can improve business results.
The Science behind a Winning Sales CultureBrad Giles
Presentation outlining the different types of salespeople and how a top performing salesperson is impacted by their strengths, skills & severity of weaknesses. Provides a brief summary of the sales assessment we have used on almost 1million salespeople around the world to determine whether they will sell. More details at www.evolutionpartners.com.au
Central tendency refers to measures that characterize the middle or center of a data set. The three most common measures of central tendency are the mean, median, and mode. The mean is the average value found by dividing the sum of all values by the number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently in the data set. These measures help analyze and understand data in a statistical analysis.
This document discusses measures of central tendency (mean, median, mode) and measures of spread (range, variance, standard deviation). It provides formulas and examples to calculate each measure. It also presents two problems, asking to calculate and compare various descriptive statistics for different data sets, such as milk yields from two cow herds and weaning weights of lambs from two breeds. A third problem asks to analyze and compare price data for rice from two markets.
This document discusses key performance indicators (KPIs) for senior staff accountant positions. It provides information on developing KPIs, including defining objectives and key result areas, identifying tasks, and determining how to measure results. The document recommends that KPIs be clearly linked to strategy, answer important questions, and empower employees. It also discusses different types of KPIs and mistakes to avoid when creating KPIs, such as having too many. The document directs the reader to an online source for additional KPI samples and materials.
Measure of dispersion part II ( Standard Deviation, variance, coefficient of ...Shakehand with Life
This tutorial gives the detailed explanation measure of dispersion part II (standard deviation, properties of standard deviation, variance, and coefficient of variation). It also explains why std. deviation is used widely in place of variance. This tutorial also teaches the MS excel commands of calculation in excel.
Training Slides of KPIs, Work flow & evaluating performances discussing the importance of KPI.
For further information regarding the course, please contact:
info@asia-masters.com
www.asia-masters.com
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help boost feelings of calmness, happiness and focus.
This document discusses key performance indicators (KPIs) for senior accountant positions. It provides steps for creating KPIs for senior accountants, including defining objectives, identifying key result areas and tasks, and determining how to measure results. The document warns against creating too many KPIs and notes that KPIs should be linked to strategy and empower employees. It also lists different types of KPIs and provides a link to additional KPI materials and resources.
Origins of the Marketing Intelligence Engine (INBOUND 2016)PR 20/20
The velocity of change in the marketing industry is accelerating, but what we see today is elementary when we consider the potential of what comes next. This session provides a glimpse into the future of marketing, and the opportunities that exist for those who can harness the power of artificial intelligence and cognitive technology like IBM's Watson. They will be able to do more with less, run personalized campaigns of unprecedented complexity, and analyze massive data sets to predict outcomes. The opportunities are endless for those with the will and vision to transform the industry. Attendees will:
- Learn what the disruption of other industries can teach us about the inevitable impact artificial intelligence will have on the marketing industry.
- Discover existing marketing technologies using artificial intelligence to make marketing more efficient and effective.
- Get inspired to explore what’s possible for the future of marketing, as well as their businesses and careers.
The document provides information on key performance indicators (KPIs). It discusses why KPIs are important for tracking business performance, how to develop a balanced scorecard to measure KPIs across different perspectives like customers, internal processes, learning and growth, and financials. It also provides examples of generic KPI measures and how to implement KPIs through defining strategic goals and drivers, developing new measures, analyzing and reporting on trends, and driving continuous improvement.
One of the best ways to analyze any process is to plot the data. Different graphs can reveal different characteristics of your data such as the central tendency, the dispersion and the general shape for thedistribution.
Data Analyst Interview Questions & AnswersSatyam Jaiswal
Practice Best Data Analyst Interview Questions for the best preparation of the data analyst interview. these interview questions are very popular and asked various times in data analyst interview.
Top 30 Data Analyst Interview Questions.pdfShaikSikindar1
Data Analytics has emerged has one of the central aspects of business operations. Consequently, the quest to grab professional positions within the Data Analytics domain has assumed unimaginable proportions. So if you too happen to be someone who is desirous of making through a Data Analyst .
Unit 2_ Descriptive Analytics for MBA .pptxJANNU VINAY
This document provides an overview of descriptive analytics and data visualization. It discusses descriptive statistics such as measures of central tendency (mean, median, mode) and variability. It also covers data visualization techniques like charts, graphs and dashboards. Key topics include univariate, bivariate and multivariate analysis for data visualization, different types of visualizations, and how to create charts in Microsoft Excel. The document is intended to introduce readers to the fundamental concepts and tools used in descriptive analytics.
Data Processing & Explain each term in details.pptxPratikshaSurve4
Data processing involves converting raw data into useful information through various steps. It includes collecting data through surveys or experiments, cleaning and organizing the data, analyzing it using statistical tools or software, interpreting the results, and presenting findings visually through tables, charts and graphs. The goal is to gain insights and knowledge from the data that can help inform decisions. Common data analysis types are descriptive, inferential, exploratory, diagnostic and predictive analysis. Data analysis is important for businesses as it allows for better customer targeting, more accurate decision making, reduced costs, and improved problem solving.
BA is used to gain insights that inform business decisions and can be used to automate and optimize business processes. Data-driven companies treat their data as a corporate asset and leverage it for a competitive advantage. Successful business analytics depends on data quality, skilled analysts who understand the technologies and the business, and an organizational commitment to data-driven decision-making.
Business analytics examples
Business analytics techniques break down into two main areas. The first is basic business intelligence. This involves examining historical data to get a sense of how a business department, team or staff member performed over a particular time. This is a mature practice that most enterprises are fairly accomplished at using.
This document provides an introduction to data science concepts. It discusses the components of data science including statistics, visualization, data engineering, advanced computing, and machine learning. It also covers the advantages and disadvantages of data science, as well as common applications. Finally, it outlines the six phases of the data science process: framing the problem, collecting and processing data, exploring and analyzing data, communicating results, and measuring effectiveness.
Data Science & AI Road Map by Python & Computer science tutor in MalaysiaAhmed Elmalla
The slides were used in a trial session for a student aiming to learn python to do Data science projects .
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DATA ANALYSIS Presentation Computing Fundamentals.pptxAmarAbbasShah1
This document discusses data analysis and provides details on the following:
- It defines data analysis and provides examples of its use.
- It describes the four main types of data analysis: descriptive, diagnostic, predictive, and prescriptive.
- It outlines the six step data analysis process: data requirement gathering, data collection, data cleaning, analyzing data, data interpretation, and data visualization.
- It provides examples to illustrate each type and step of the analysis process.
- It also lists some commonly used data analysis tools.
The document discusses the seven basic quality control tools: (1) flow charts visually illustrate process steps; (2) check sheets collect data at its source; (3) histograms graphically show data distribution; (4) Pareto charts identify the most important causes; (5) cause-and-effect diagrams help determine root causes; (6) control charts distinguish common from special causes of variation; and (7) scatter diagrams study relationships between two variables. Examples are provided for each tool to demonstrate how they are constructed and interpreted for quality improvement.
This document discusses data analytics and related concepts. It defines data and information, explaining that data becomes information when it is organized and analyzed to be useful. It then discusses how data is everywhere and the value of data analysis skills. The rest of the document outlines the methodology of data analytics, including data collection, management, cleaning, exploratory analysis, modeling, mining, and visualization. It provides examples of how data analytics is used in healthcare and travel to optimize processes and customer experiences.
Data Analysis Methods 101 - Turning Raw Data Into Actionable InsightsDataSpace Academy
Data analytics is powerful for organisations. It can help companies improve their overall efficiency and effectiveness. The blog offers a step-by-step narration of the data analysis methods that will help you to comprehend the fundamentals of an analytics project.
Data science involves analyzing data to extract meaningful insights. It uses principles from fields like mathematics, statistics, and computer science. Data scientists analyze large amounts of data to answer questions about what happened, why it happened, and what will happen. This helps generate meaning from data. There are different types of data analysis including descriptive analysis, which looks at past data, diagnostic analysis, which finds causes of past events, and predictive analysis, which forecasts future trends. The data analysis process involves specifying requirements, collecting and cleaning data, analyzing it, interpreting results, and reporting findings. Tools like SAS, Excel, R and Python are used for these tasks.
Data science uses techniques like machine learning and AI to extract meaningful insights from large, complex datasets. It relies on applied mathematics, statistics, and programming to analyze big data. Common data science tools include SAS for statistical analysis, Apache Spark for large-scale processing, BigML for machine learning modeling, Excel for visualization and basic analytics, and programming libraries like TensorFlow, Scikit-learn, and NLTK. These tools help data scientists extract knowledge and make predictions from huge amounts of data.
IRJET - An Overview of Machine Learning Algorithms for Data ScienceIRJET Journal
This document provides an overview of machine learning algorithms that are commonly used for data science. It discusses both supervised and unsupervised algorithms. For supervised algorithms, it describes decision trees, k-nearest neighbors, and linear regression. Decision trees create a hierarchical structure to classify data, k-nearest neighbors classifies new data based on similarity to existing data, and linear regression finds a linear relationship between variables. Unsupervised algorithms like clustering are also briefly mentioned. The document aims to familiarize data science enthusiasts with basic machine learning techniques.
This document outlines a data analytics approach including data exploration, model development, and interpretation. Data exploration involves visualizing and analyzing data to uncover patterns and insights. Model development is an iterative process of testing models until one fits the desired criteria. Data interpretation turns analysis results into a presentable format to gain clear insights for business strategies such as reporting findings in a dashboard.
This document discusses various tools and methodologies for process improvement, including the Deming Cycle (Plan-Do-Study-Act), flowcharts, check sheets, histograms, Pareto diagrams, cause-and-effect diagrams, scatter diagrams, run charts, control charts, Kaizen blitz, poka-yoke, process simulation, and skills for team leaders and members. It provides descriptions and examples of how each tool is used to define problems, measure processes, analyze data, improve processes, and ensure changes are standardized and monitored.
The document discusses 7 planning tools used in Total Quality Management (TQM): fishbone diagram, Pareto chart, checksheet, histogram, control charts, scatter diagram, and flow charts. It provides descriptions of each tool, including what they are used for and how to construct them. The fishbone diagram is used to identify and relate causes of a problem. The Pareto chart identifies the most important causes to address. The checksheet collects quantitative or qualitative data. Histograms show the distribution of data, and control charts monitor process stability. Scatter diagrams show relationships between variables. Flow charts map out process steps.
Lecture 3
Statistical Process
Control (SPC)
Data collection for Six SigmaData are simply facts and figures without context or interpretation.Information refers to useful or meaningful patterns found in the data.Knowledge represents information of sufficient quality and/or quantity that actions can be taken based on the information.If data are not collected and used wisely, their vary existence can lead to activities that are ineffective and possibly even counterproductive.An organization collects data & reacts whenever an out-of-specification condition occurs.
“Common cause” & “ special cause” variation
There are two causes of process variations:
1) Common cause variation: This variation is due to the process only. It may not tell you whether the process meets the needs of the customer unless it is compared with the specification. This can be improved by focusing on the process.
2) Special cause variation: This variation is due the individual employee, if the point is beyond specification limits. In this case the focus should be about what happened relative to the individual employee as though it were a “special” condition.
Attribute versus Variable Data
Attribute data: It is a data with yes or no decision such as:whether an iten passed or failed a testpass/fail, go/no go gaging, true/false, accept/reject. There are no quantifiable values
Variable data: are related to measurements with quantifiable values such as:Diameter of a part which has been machinedlength or thickness of the machined part
The success of Six SigmaThe success of Six Sigma depends upon knowing the difference between special & common cause variations and how the organization reacts to the data.If the management focuses on wrong cause of variation, it can lead to waste of time (firefighting).It can also effect employee motivation & morale.Reacting to one data point that do not meet the specification limit can be counterproductive and very expensive.Do not use “firefighting” actions just because the data point is out of specification limits. It must first be determined whether the condition is common or special cause.
Example of variability due to common causeControl limits are calculated from the sample data.There are no data points outside the control limits therefore there are no special causes within the data.The source of variation in this case is “common cause” due to process.
Type of firefighting done by management before evaluating the cause of variabilityProduction supervisors might constantly review production output by employee, machine, product line, work shift etc.An administrative assistant’s daily output & memo’s may be monitored.The average time per call may be monitored in a call center.The efficiency of computer programmers may be monitored by tracking “lines of code produced per day”.
All of these actions would be a waste of time if the cause of variability is “common cause” and due to the process rather than individu ...
Machine learning can be used to predict whether a user will purchase a book on an online book store. Features about the user, book, and user-book interactions can be generated and used in a machine learning model. A multi-stage modeling approach could first predict if a user will view a book, and then predict if they will purchase it, with the predicted view probability as an additional feature. Decision trees, logistic regression, or other classification algorithms could be used to build models at each stage. This approach aims to leverage user data to provide personalized book recommendations.
Continuous Improvement Infographics for LearningCIToolkit
The purpose of this section is to provide all the continuous improvement tools in an infographic format. These flashcards are easy to read and understand, and very useful if you are looking for brief, concise, and to-the-point summaries. They are quick refreshers for continuous improvement and can speed up the learning process.
Continuous Improvement Posters for LearningCIToolkit
The intention of this section is to provide all the continuous improvement tools in a poster format that is easy to print and share. These posters are great tools for training, sharing and posting, and can also be distributed as hand-outs during continuous improvement workshops.
Simplifying Complexity: How the Four-Field Matrix Reshapes ThinkingCIToolkit
A Four Field Matrix is an effective model for planning, organizing and making decisions. It is a two-dimensional chart that consists of four equal-sized quadrants, each will describe different aspects of information.
Unlocking Productivity and Personal Growth through the Importance-Urgency MatrixCIToolkit
Importance Urgency Matrix is an effective method of organizing priorities. It is a two-dimensional chart that is used to prioritize work activities as well as personal activities.
Measuring True Process Yield using Robust Yield MetricsCIToolkit
Process yield measures should be able to expose even the smallest inefficiencies within a process, empowering operations to understand their true process yield in order to set realistic targets for improvement. Many organizations employ two primary measures of process yield: First Time Yield (FTY) and Final Yield (FY).
Beyond the Five Whys: Exploring the Hierarchical Causes with the Why-Why DiagramCIToolkit
A why-why diagram is used to identify the root causes of a problem when there are multiple factors to consider. There may be multiple answers at each stage, and each of these answers need to go through a separate process of the why-whys analysis. It is an extension of the 5 Whys approach where they are similar in that they both ask the same Why question multiple times. #WhyWhyDiagram
How-How Diagram: A Practical Approach to Problem ResolutionCIToolkit
How- How Diagram is used when seeking a practical solution to a problem. It works by repeatedly asking: How can this be solved. Multiple answers can be given for a single question, and therefore the result can be represented in a hierarchical tree format.
From Goals to Actions: Uncovering the Key Components of Improvement RoadmapsCIToolkit
An improvement roadmap is an approach used to achieve improvement. It is used to guide through the implementation of a long-term improvement journey. It helps us to understand where we are now as well as where we want to go.
Paired Comparison Analysis: A Practical Tool for Evaluating Options and Prior...CIToolkit
Paired Comparison Analysis is an activity for evaluating a small range of options by comparing them against each other. It is an easy and useful tool for rating and ranking alternatives for decision making where evaluation criteria are subjective.
From Red to Green: Enhancing Decision-Making with Traffic Light AssessmentCIToolkit
Traffic Light Assessment is a rating system for evaluating the performance of a process or variable in relation to a goal. It is a good way to communicate information and have the advantage of being universally recognized by everyone.
Mind Mapping: A Visual Approach to Organize Ideas and ThoughtsCIToolkit
Visually organizing ideas, thoughts and information around a single topic or problem. Mind mapping has many applications in personal, professional and educational situations.
Adapting to Change: Using PEST Analysis for Better Decision-MakingCIToolkit
A strategic and structured planning tool for evaluating the external environment of an organization. PEST stands for Political, Economic, Social, and Technological external factors.
The Role of Box Plots in Comparing Multiple Data SetsCIToolkit
A box plot is a graph that shows the frequency of numeric data values. It can be drawn either horizontally or vertically. It is referred to as a Box-and-Whisker Plot.
Exploring Variable Relationships with Scatter Diagram AnalysisCIToolkit
A Scatter Diagram is a way of showing whether two variables are correlated or related to each other. It shows patterns in the relationship that cannot be seen by just looking at the data. A scatter diagram uses a two-axis chart to represent data.
The Role of Histograms in Exploring Data InsightsCIToolkit
A graph which shows the frequency of continuous data values. Histograms are mainly used to explore data as well as to present the data in an easy and understandable manner. They are often used as the first step to determine the underlying probability distribution of a data set or a sample.
Leveraging Gap Analysis for Continuous ImprovementCIToolkit
Gap analysis compares two different states of something, the current state and the future state. It is mainly used to assess where a company or process is today, where it needs to be in the future, and what needed to be there. Gap analysis is also known as need analysis or need assessment.
Flowcharting: The Three Common Types of FlowchartsCIToolkit
A graphical tool that illustrates the flow of a business process and the relationships between its activities. It helps you and your team to understand the activities and decisions, and thus, perform the tasks correctly and in the right order.
Yokoten: Enhancing Performance through Best Practice SharingCIToolkit
Everybody can benefit from the successes of others. Developing a best practice program for your company is an integral part of becoming a world-class performer in your industry. The more you can do to promote the creation and sharing of great ideas within your company, the better your performance will be in the long run and the more engaged your employees will be. You need also to consider what other world-class organizations are doing to become even more innovative and competitive.
Value Analysis: How Lean Thinking Defines ValueCIToolkit
Value Analysis as per Lean definition focuses on what adds value to business processes as perceived by the customer. A process that does not add value to the product or service should be redesigned or eliminated altogether.
SpatzAI.com empowers teams to resolve their minor conflicts quickly and effectively with its real-time, AI-driven intervention app and platform.
By breaking down micro-conflicts into 3 phases (tokens), SpatzAI ensures open communication and psychological safety, creating a collaborative environment where bold ideas can thrive and measured. Our data-driven approach and team-assisted review system enhance accountability, transforming potential spats into opportunities for growth.
Mentoring - A journey of growth & developmentAlex Clapson
If you're looking to embark on a journey of growth & development, Mentoring could
offer excellent way forward for you. It's an opportunity to engage in a profound
learning experience that extends beyond immediate solutions to foster long-term
growth & transformation.
ANIn Chennai June 2024 | Right Business strategy is foundational for Successf...AgileNetwork
Agile Network India - Chennai
Title: Right Business strategy is foundational for Successful Digital Transformation
Date: 22nd June 2024
Hosted by : Siara Tech Solutions Pvt Ltd
Corporate innovation with Startups made simple with Pitchworks VC StudioGokul Rangarajan
In this write up we will talk about why corporates need to innovate, why most of them of failing and need to startups and corporate start collaborating with each other for survival
At the end of the conversation the CIO asked us 3 questions which sparked us to write this blog.
1 Do my organisation need innovation ?
2 Even if I need Innovation why are so many other corporates of our size fail in innovation ?
3 How can I test it in most cost effective way ?
First let's address the Elephant in the room, is Innovation optional ?
Relevance for customers
Building Business Reslience
competitive advantage
Corporate innovation is essential for businesses striving to remain relevant and competitive in today's rapidly evolving market. By continuously developing new products, services, and processes, companies can better meet the changing needs and preferences of their customers. For instance, Apple's regular release of new iPhone models keeps them at the forefront of consumer technology, while Amazon's introduction of Prime services has revolutionized online shopping convenience. Statistics show that innovative companies are 2.5 times more likely to have high-performance outcomes compared to their peers.
This proactive approach not only helps in retaining existing customers but also attracts new ones, ensuring sustained growth and market presence.
Furthermore, innovation fosters a culture of creativity and adaptability within organizations, enabling them to quickly respond to emerging trends and disruptions. In essence, corporate innovation is the driving force that keeps companies aligned with customer expectations, ultimately leading to long-term success and relevance.
Business Resilience
Building business resilience is paramount for companies looking to thrive amidst uncertainties and disruptions. Corporate innovation plays a crucial role in fostering this resilience by enabling businesses to adapt, evolve, and maintain continuity during challenging times. For instance, during the COVID-19 pandemic, many companies that swiftly innovated their business models, such as shifting to remote work or expanding e-commerce capabilities, managed to survive and even thrive. According to a McKinsey report, organizations that prioritize innovation are 30% more likely to be high-growth companies. Innovation not only helps in developing new revenue streams but also in creating more efficient processes and resilient supply chains. This agility allows companies to quickly pivot in response to market changes, ensuring they can weather economic downturns, technological disruptions, and other unforeseen challenges. Therefore, corporate innovation is not just a strategy for growth but a vital component of building a robust and resilient business capable of sustaining long-term success.
2. Continuous Improvement Toolkit . www.citoolkit.com
The Continuous Improvement Map
Check Sheets
Data
Collection
Process MappingFlowcharting
Flow Process Charts**
Just in Time
Control Charts
Mistake Proofing
Relations Mapping
Understanding
Performance**
Fishbone Diagram
Design of Experiment
Implementing
Solutions***
Group Creativity
Brainstorming Attribute Analysis
Selecting & Decision Making
Decision Tree
Cost Benefit Analysis
Voting
Planning & Project Management*
Kaizen Events
Quick Changeover
Managing
Risk
FMEA
PDPC
RAID Log*
Observations
Focus Groups
Understanding
Cause & Effect
Pareto Analysis
IDEF0
5 Whys
Kano
KPIs
Lean Measures
Importance-Urgency Mapping
Waste Analysis**
Fault Tree Analysis
Morphological Analysis
Benchmarking***
SCAMPER***
Matrix Diagram
Confidence Intervals
Pugh Matrix
SIPOC*
Prioritization Matrix
Stakeholder Analysis
Critical-to Tree
Paired Comparison
Improvement Roadmaps
Interviews
Quality Function Deployment
Graphical Analysis
Lateral Thinking
Hypothesis Testing
Visual Management
Reliability Analysis
Cross Training
Tree Diagram*
ANOVA
Gap Analysis*
Traffic Light Assessment
TPN Analysis
Decision Balance Sheet
Risk Analysis*
Automation
Simulation
Service Blueprints
DMAIC
Product Family MatrixRun Charts
TPM
Control Planning
Chi-Square
SWOT Analysis
Capability Indices
Policy Deployment
Data collection planner*
Affinity DiagramQuestionnaires
Probability Distributions
Bottleneck Analysis
MSA
Descriptive Statistics
Cost of Quality*
Process Yield
Histograms 5S
Pick Chart
Portfolio Matrix
Four Field Matrix
Root Cause Analysis Data Mining
How-How Diagram***Sampling
Spaghetti **
Mind Mapping*
Project Charter
PDCA
Designing & Analyzing Processes
CorrelationScatter Plots Regression
Gantt Charts
Activity NetworksRACI Matrix
PERT/CPMDaily Planning
MOST
Standard work Document controlA3 Thinking
Multi vari Studies
OEE
Earned Value
Delphi Method
Time Value Map**
Value Stream Mapping**
Force Field Analysis
Payoff Matrix
Suggestion systems Five Ws
Process Redesign
Break-even Analysis
Value Analysis**
FlowPull
Ergonomics
3. Continuous Improvement Toolkit . www.citoolkit.com
Statistics is concerned with the describing, interpretation and
analyzing of data.
It is, therefore, an essential element in any improvement
process.
Statistics is often categorized into descriptive and inferential
statistics.
It uses analytical methods which provide
the math to model and predict variation.
It uses graphical methods to help making
numbers visible for communication
purposes.
- Descriptive Statistics
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Why do we Need Statistics?
To find why a process behaves the way it does.
To find why it produces defective goods or services.
To center our processes on ‘Target’ or ‘Nominal’.
To check the accuracy and precision of the process.
To prevent problems caused by assignable causes
of variation.
To reduce variability and improve process capability.
To know the truth about the real world.
- Descriptive Statistics
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Descriptive Statistics:
Methods of describing the characteristics of a data set.
Useful because they allow you to make sense of the data.
Helps exploring and making conclusions about the data in order
to make rational decisions.
Includes calculating things such as the average of the data, its
spread and the shape it produces.
- Descriptive Statistics
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For example, we may be concerned about describing:
• The weight of a product in a production line.
• The time taken to process an application.
- Descriptive Statistics
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Descriptive statistics involves describing, summarizing and
organizing the data so it can be easily understood.
Graphical displays are often used along with the quantitative
measures to enable clarity of communication.
- Descriptive Statistics
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When analyzing a graphical display, you can draw conclusions
based on several characteristics of the graph.
You may ask questions such ask:
• Where is the approximate middle, or center, of the graph?
• How spread out are the data values on the graph?
• What is the overall shape of the graph?
• Does it have any interesting patterns?
- Descriptive Statistics
9. Continuous Improvement Toolkit . www.citoolkit.com
Outlier:
A data point that is significantly greater or smaller than other
data points in a data set.
It is useful when analyzing data to identify outliers
They may affect the calculation of descriptive
statistics.
Outliers can occur in any given data set and in
any distribution.
- Descriptive Statistics
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Outlier:
The easiest way to detect them is by graphing the data or using
graphical methods such as:
• Histograms.
• Boxplots.
• Normal probability plots.
- Descriptive Statistics
*●
11. Continuous Improvement Toolkit . www.citoolkit.com
Outlier:
Outliers may indicate an experimental error or incorrect
recording of data.
They may also occur by chance.
• It may be normal to have high or low data points.
You need to decide whether to exclude them
before carrying out your analysis.
• An outlier should be excluded if it is due to
measurement or human error.
- Descriptive Statistics
12. Continuous Improvement Toolkit . www.citoolkit.com
Outlier:
This example is about the time taken to process a sample of
applications.
- Descriptive Statistics
Outlier
0 1 2 3 4 5 6 7 8 9
2.8 8.7 0.7 4.9 3.4 2.1 4.0
It is clear that one data point is far distant from the rest of the values.
This point is an ‘outlier’
13. Continuous Improvement Toolkit . www.citoolkit.com
The following measures are used to describe a data set:
Measures of position (also referred to as central tendency or
location measures).
Measures of spread (also referred to as variability or dispersion
measures).
Measures of shape.
- Descriptive Statistics
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If assignable causes of variation are affecting the process, we
will see changes in:
• Position.
• Spread.
• Shape.
• Any combination of the three.
- Descriptive Statistics
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Measures of Position:
Position Statistics measure the data central tendency.
Central tendency refers to where the data is centered.
You may have calculated an average of some kind.
Despite the common use of average, there are different
statistics by which we can describe the average of a data set:
• Mean.
• Median.
• Mode.
- Descriptive Statistics
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Mean:
The total of all the values divided by the size of the data set.
It is the most commonly used statistic of position.
It is easy to understand and calculate.
It works well when the distribution is symmetric and there are
no outliers.
The mean of a sample is denoted by ‘x-bar’.
The mean of a population is denoted by ‘μ’.
- Descriptive Statistics
0 1 2 3 4 5 6 7 8 9
Mean
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Median:
The middle value where exactly half of the data values are
above it and half are below it.
Less widely used.
A useful statistic due to its robustness.
It can reduce the effect of outliers.
Often used when the data is nonsymmetrical.
Ensure that the values are ordered before calculation.
With an even number of values, the median is the mean of the
two middle values.
- Descriptive Statistics
0 1 2 3 4 5 6 7 8 9
MeanMedian
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Why can the mean and median be different?
- Descriptive Statistics
0 1 2 3 4 5 6 7 8 9
MeanMedian
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Mode:
The value that occurs the most often in a data set.
It is rarely used as a central tendency measure
It is more useful to distinguish between unimodal and
multimodal distributions
• When data has more than one peak.
- Descriptive Statistics
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Measures of Spread:
The Spread refers to how the data deviates from the position
measure.
It gives an indication of the amount of variation in the process.
• An important indicator of quality.
• Used to control process variability and improve quality.
All manufacturing and transactional
processes are variable to some degree.
There are different statistics by which
we can describe the spread of a data set:
• Range.
• Standard deviation.
- Descriptive Statistics
Spread
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Range:
The difference between the highest and the lowest values.
The simplest measure of variability.
Often denoted by ‘R’.
It is good enough in many practical cases.
It does not make full use of the available data.
It can be misleading when the data is skewed or in the presence
of outliers.
• Just one outlier will increase
the range dramatically.
- Descriptive Statistics
0 1 2 3 4 5 6 7 8 9
Range
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Standard Deviation:
The average distance of the data points from their own mean.
A low standard deviation indicates that the data points are
clustered around the mean.
A large standard deviation indicates that they are widely
scattered around the mean.
The standard deviation of a sample is
denoted by ‘s’.
The standard deviation of a population
is denoted by “μ”.
- Descriptive Statistics
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Standard Deviation:
Perceived as difficult to understand because it is not easy to
picture what it is.
It is however a more robust measure of variability.
Standard deviation is computed as follows:
- Descriptive Statistics
Mean (x-bar)
s = standard deviation
x = mean
x = values of the data set
n = size of the data set
s =
∑ ( x – x )2
n - 1
25. Continuous Improvement Toolkit . www.citoolkit.com
Exercise:
This example is about the time taken to process a sample of
applications.
Find the mean, median, range and standard deviation for the
following set of data: 2.8, 8.7, 0.7, 4.9, 3.4, 2.1 & 4.0.
- Descriptive Statistics
Time allowed: 10 minutes
26. Continuous Improvement Toolkit . www.citoolkit.com
If someone hands you a sheet of data and asks you to find the
mean, median, range and standard deviation, what do you do?
- Descriptive Statistics
21 19 20 24 23 21 26 23
25 24 19 19 21 19 25 19
23 23 15 22 23 20 14 20
15 19 20 21 17 15 16 19
13 17 19 17 22 20 18 16
17 18 21 21 17 20 21 21
21 17 17 19 21 22 25 20
19 20 24 28 26 26 25 24
27. Continuous Improvement Toolkit . www.citoolkit.com
Measures of Shape:
Data can be plotted into a histogram to have a general idea of
its shape, or distribution.
The shape can reveal a lot of information about the data.
Data will always follow some know distribution.
- Descriptive Statistics
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Measures of Shape:
It may be symmetrical or nonsymmetrical.
In a symmetrical distribution, the two sides of the distribution
are a mirror image of each other.
Examples of symmetrical distributions include:
• Uniform.
• Normal.
• Camel-back.
• Bow-tie shaped.
- Descriptive Statistics
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Measures of Shape:
The shape helps identifying which descriptive statistic is more
appropriate to use in a given situation.
If the data is symmetrical, then we may use the mean or median
to measure the central tendency as they are almost equal.
If the data is skewed, then the median will be a more
appropriate to measure the central tendency.
Two common statistics that measure the shape of the data:
• Skewness.
• Kurtosis.
- Descriptive Statistics
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Skewness:
Describes whether the data is distributed symmetrically around
the mean.
A skewness value of zero indicates perfect symmetry.
A negative value implies left-skewed data.
A positive value implies right-skewed data.
- Descriptive Statistics
XXX
XXX
XXX
XX
XX
X
X
X
X
XXX
X
X
X
X
XXX
XXX
XXX
XX
XX
X
X
X
X
XXX
X
X
X
X
(+) – SK > 0 (-) – SK < 0
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Kurtosis:
Measures the degree of flatness (or peakness) of the shape.
When the data values are clustered around the middle, then the
distribution is more peaked.
• A greater kurtosis value.
When the data values are spread around more evenly, then the
distribution is more flatted.
• A smaller kurtosis values.
- Descriptive Statistics
XXXXX
XXX
XXX
X
X
X
XXXXX
XXX
XXXX
XX
XX
X
XXX
XXX
XXX
XX
XX
X
X
X
(-) Platykurtic (0) Mesokurtic (+) Leptokurtic
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Skewness and kurtosis statistics can be evaluated visually via a
histogram.
They can also be calculated by hand.
This is generally unnecessary with modern statistical software
(such as Minitab).
- Descriptive Statistics
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Further Information:
Variance is a measure of the variation around the mean.
It measures how far a set of data points are spread out from
their mean.
The units are the square of the units used for the original data.
• For example, a variable measured in meters will have a variance
measured in meters squared.
It is the square of the standard deviation.
- Descriptive Statistics
Variance = s2
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Further Information:
The Inter Quartile Range is also used to measure
variability.
Quartiles divide an ordered data set into 4 parts.
Each contains 25% of the data.
The inter quartile range contains the middle
50% of the data (i.e. Q3-Q1).
It is often used when the data is not normally
distributed.
- Descriptive Statistics
25%
Interquartile Range
25%
25%
25%
50%
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Minitab is a statistical software that allows you to enter your
data to perform a wide range of statistical analyses.
It can be used to calculate many types of descriptive statistics.
It tells you a lot about your data in order to make more rational
decisions.
Descriptive statistics summaries in Minitab
can be either quantitative or visual.
- Descriptive Statistics in Minitab
Descriptive Statistics
36. Continuous Improvement Toolkit . www.citoolkit.com
Example:
A hospital is seeking to detect the presence of high glucose
levels in patients at admission.
You may use the glucose_level_fasting worksheet or use data
that you have collected yourself.
Remember to copy the data from
the excel sheet and paste it into
Minitab worksheet.
- Descriptive Statistics in Minitab
79 72 77 85 76 120 78 94
93 70 79 75 68 73 79 85
98 77 77 88 79 79 70 113
75 80 74 83 85 79 87 82
104 106 81 76 68 72 61 95
78 106 84 70 96 70 90 98
69 60 74 67 71 75 105 79
71 75 131 80 75 52 152 106
81 96
37. Continuous Improvement Toolkit . www.citoolkit.com
Example:
To create a quantitative summary of your data:
• Select Stat > Basic Statistics > Display Descriptive Statistics.
• Select the variable to be analyzed, in this case ‘glucose level’.
• Click OK.
Here is a screenshot of the various
descriptive statistics you may
choose when doing your analysis.
- Descriptive Statistics in Minitab
38. Continuous Improvement Toolkit . www.citoolkit.com
Example:
Here is a screenshot of the example result:
- Descriptive Statistics in Minitab
Quantitative Summary
39. Continuous Improvement Toolkit . www.citoolkit.com
Example:
To create a visual summary of your data:
• Select Stat > Basic Statistics > Graphical Summary.
• Select the variable to be analyzed, in this case ‘glucose level’.
• Click OK.
Here is a screenshot
of the example result:
- Descriptive Statistics in Minitab
40. Continuous Improvement Toolkit . www.citoolkit.com
Example:
By default, Minitab fits a normal distribution curve to the
histogram.
A boxplot will also be shown to
display the four quartiles of the
data.
The 95% confidence intervals are
also shown to illustrate where the
mean and median of the population
lie.
- Descriptive Statistics in Minitab
41. Continuous Improvement Toolkit . www.citoolkit.com
Example:
Mean, standard deviation, sample size, and other descriptive
statistic values are shown in the adjacent data table.
The skewed distribution shows the
differences that can occur between
the mean and median.
The mean is pulled to the right by the
high value outliers.
The positive value for skewness indicates
a positive skew of the data set.
- Descriptive Statistics in Minitab