This document defines and explains key statistical concepts including measures of central tendency (mean, median, mode), measures of dispersion (range, standard deviation), and properties of distributions (skewness, symmetry). It provides examples of calculating the mean, median, mode, and standard deviation. It also describes the empirical rule and how a certain percentage of values in a normal distribution fall within 1, 2, or 3 standard deviations of the mean.
Multiple Correlation Coefficient denoting a correlation of one variable with multiple other variables. The Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. This presentation explains the concept of multiple correlation and its computation process.
This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently. Examples are given demonstrating how to calculate each measure for both individual values and grouped data.
This document provides an overview of key concepts in probability. It defines probability as the likelihood of an event occurring, expressed as a number between 0 and 1. It discusses common probability terms like experiment, outcome, sample space, event, and sample point. It also covers different types of probability like classical, statistical, and subjective probability. Additionally, it explains concepts like independent and mutually exclusive events, conditional probability, and Bayes' theorem. It concludes by discussing some applications of probability in fields like statistics, biology, information theory, and operations research.
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.
The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean and standard deviation. Many real-world variables are approximately normally distributed. The standard normal distribution refers to a normal distribution with a mean of 0 and standard deviation of 1. The normal distribution is commonly used to model variables and calculate probabilities related to areas under the normal curve.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.
Multiple Correlation Coefficient denoting a correlation of one variable with multiple other variables. The Multiple Correlation Coefficient, R, is a measure of the strength of the association between the independent (explanatory) variables and the one dependent (prediction) variable. This presentation explains the concept of multiple correlation and its computation process.
This document discusses various measures of dispersion in statistics including range, mean deviation, variance, and standard deviation. It provides definitions and formulas for calculating each measure along with examples using both ungrouped and grouped frequency distribution data. Box-and-whisker plots are also introduced as a graphical method to display the five number summary of a data set including minimum, quartiles, and maximum values.
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the sum of all values divided by the number of values and is the most widely used measure. The median is the middle value when data is arranged from lowest to highest. The mode is the value that occurs most frequently. Examples are given demonstrating how to calculate each measure for both individual values and grouped data.
This document provides an overview of key concepts in probability. It defines probability as the likelihood of an event occurring, expressed as a number between 0 and 1. It discusses common probability terms like experiment, outcome, sample space, event, and sample point. It also covers different types of probability like classical, statistical, and subjective probability. Additionally, it explains concepts like independent and mutually exclusive events, conditional probability, and Bayes' theorem. It concludes by discussing some applications of probability in fields like statistics, biology, information theory, and operations research.
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.
The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is defined by its mean and standard deviation. Many real-world variables are approximately normally distributed. The standard normal distribution refers to a normal distribution with a mean of 0 and standard deviation of 1. The normal distribution is commonly used to model variables and calculate probabilities related to areas under the normal curve.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
The chi-square distribution is used to test hypotheses about categorical data. It is defined as the sum of the squares of the differences between observed and expected frequencies divided by the expected frequencies. The chi-square distribution depends on the degrees of freedom, with each number of degrees of freedom having a different distribution. The chi-square test can be used to test goodness of fit, independence, and homogeneity. It requires data to be in the form of frequencies in a contingency table and assumes independence between observations.
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
This document provides an overview of non-parametric statistics. It defines non-parametric tests as those that make fewer assumptions than parametric tests, such as not assuming a normal distribution. The document compares and contrasts parametric and non-parametric tests. It then explains several common non-parametric tests - the Mann-Whitney U test, Wilcoxon signed-rank test, sign test, and Kruskal-Wallis test - and provides examples of how to perform and interpret each test.
This document provides an overview of analysis of variance (ANOVA). It introduces ANOVA and its key concepts, including its development by Ronald Fisher. It defines ANOVA and distinguishes between one-way and two-way ANOVA. It outlines the assumptions, techniques, and examples of how to perform one-way and two-way ANOVA. It also discusses the uses, advantages, and limitations of ANOVA for analyzing differences between multiple means and factors.
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
This document presents information about regression analysis. It defines regression as the dependence of one variable on another and lists the objectives as defining regression, describing its types (simple, multiple, linear), assumptions, models (deterministic, probabilistic), and the method of least squares. Examples are provided to illustrate simple regression of computer speed on processor speed. Formulas are given to calculate the regression coefficients and lines for predicting y from x and x from y.
This document provides an overview of statistical estimation and inference. It discusses point estimation, which provides a single value to estimate an unknown population parameter, and interval estimation, which gives a range of plausible values for the parameter. The key aspects of interval estimation are confidence intervals, which provide a probability statement about where the true population parameter lies. The document also covers important concepts like sampling distributions, the central limit theorem, and factors that influence the width of a confidence interval like sample size. Examples are provided to demonstrate calculating point estimates, confidence intervals, and dealing with independent samples.
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 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 discusses measures of central tendency, including the mean, median, and mode. It defines each measure and describes their characteristics and how to calculate them. The mean is the average value and is affected by outliers. The median is the middle value and is not affected by outliers. The mode is the most frequently occurring value. The document provides examples of calculating each measure from data sets and discusses their advantages and disadvantages.
A histogram is a graphical representation of data using bars of different heights. It summarizes a data set by dividing it into bins and plotting the count of data points in each bin. The bins are usually consecutive, non-overlapping intervals of a variable. A histogram provides a visual summary of distribution and frequency of data values. It allows comparison of measurements to specifications and assists in decision making.
This document provides an overview of sampling methods for research. It defines key terms like universe, sample, and population. It explains that sampling involves studying a subset of a larger population due to limitations of time, resources, and feasibility of studying every member. The document outlines different sampling methods like simple random sampling, stratified sampling, and cluster sampling. It notes that sampling allows for time and cost savings while still providing accurate results. However, limitations include potential inaccuracies if not done scientifically and difficulty ensuring representativeness.
The document discusses the history and definition of degrees of freedom. It states that the earliest concept of degrees of freedom was noted in the 1800s in the works of mathematician Carl Friedrich Gauss. The modern understanding was developed by statistician William Sealy Gosset in 1908, though he did not use the term. The term "degrees of freedom" became popular after English biologist Ronald Fisher began using it in 1922 when publishing reports on his work developing chi squares. Degrees of freedom represent the number of values in a study that can vary freely. They are important for understanding chi-square tests and the validity of the null hypothesis.
Measure of Central Tendency (Mean, Median, Mode and Quantiles)Salman Khan
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.
- 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.
It is most useful for the students of BBA for the subject of "Data Analysis and Modeling"/
It has covered the content of chapter- Data regression Model
Visit for more on www.ramkumarshah.com.np/
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
Mean, Median, Mode: Measures of Central Tendency Jan Nah
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total 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. Each measure provides a single number to represent the central or typical value in a data set.
This document defines and provides instructions for calculating mean, median, mode, and range for a set of numbers. It defines each term, explains the steps to calculate each, and provides examples of calculating mean, median, mode, and range for practice number sets.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
The chi-square distribution is used to test hypotheses about categorical data. It is defined as the sum of the squares of the differences between observed and expected frequencies divided by the expected frequencies. The chi-square distribution depends on the degrees of freedom, with each number of degrees of freedom having a different distribution. The chi-square test can be used to test goodness of fit, independence, and homogeneity. It requires data to be in the form of frequencies in a contingency table and assumes independence between observations.
This document discusses measures of dispersion in statistics. It defines dispersion as the extent of variation in a data set from the average value. There are two main types of dispersion - absolute and relative. Absolute measures express variation in units of the data and include range, variance, standard deviation, and quartile deviation. Relative measures allow comparison between data sets by being unit-free, such as the coefficient of variation. Key absolute measures are then explained in more detail, along with their merits and demerits.
This document provides an overview of non-parametric statistics. It defines non-parametric tests as those that make fewer assumptions than parametric tests, such as not assuming a normal distribution. The document compares and contrasts parametric and non-parametric tests. It then explains several common non-parametric tests - the Mann-Whitney U test, Wilcoxon signed-rank test, sign test, and Kruskal-Wallis test - and provides examples of how to perform and interpret each test.
This document provides an overview of analysis of variance (ANOVA). It introduces ANOVA and its key concepts, including its development by Ronald Fisher. It defines ANOVA and distinguishes between one-way and two-way ANOVA. It outlines the assumptions, techniques, and examples of how to perform one-way and two-way ANOVA. It also discusses the uses, advantages, and limitations of ANOVA for analyzing differences between multiple means and factors.
It includes various cases and practice problems related to Binomial, Poisson & Normal Distributions. Detailed information on where tp use which probability.
This document presents information about regression analysis. It defines regression as the dependence of one variable on another and lists the objectives as defining regression, describing its types (simple, multiple, linear), assumptions, models (deterministic, probabilistic), and the method of least squares. Examples are provided to illustrate simple regression of computer speed on processor speed. Formulas are given to calculate the regression coefficients and lines for predicting y from x and x from y.
This document provides an overview of statistical estimation and inference. It discusses point estimation, which provides a single value to estimate an unknown population parameter, and interval estimation, which gives a range of plausible values for the parameter. The key aspects of interval estimation are confidence intervals, which provide a probability statement about where the true population parameter lies. The document also covers important concepts like sampling distributions, the central limit theorem, and factors that influence the width of a confidence interval like sample size. Examples are provided to demonstrate calculating point estimates, confidence intervals, and dealing with independent samples.
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 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 discusses measures of central tendency, including the mean, median, and mode. It defines each measure and describes their characteristics and how to calculate them. The mean is the average value and is affected by outliers. The median is the middle value and is not affected by outliers. The mode is the most frequently occurring value. The document provides examples of calculating each measure from data sets and discusses their advantages and disadvantages.
A histogram is a graphical representation of data using bars of different heights. It summarizes a data set by dividing it into bins and plotting the count of data points in each bin. The bins are usually consecutive, non-overlapping intervals of a variable. A histogram provides a visual summary of distribution and frequency of data values. It allows comparison of measurements to specifications and assists in decision making.
This document provides an overview of sampling methods for research. It defines key terms like universe, sample, and population. It explains that sampling involves studying a subset of a larger population due to limitations of time, resources, and feasibility of studying every member. The document outlines different sampling methods like simple random sampling, stratified sampling, and cluster sampling. It notes that sampling allows for time and cost savings while still providing accurate results. However, limitations include potential inaccuracies if not done scientifically and difficulty ensuring representativeness.
The document discusses the history and definition of degrees of freedom. It states that the earliest concept of degrees of freedom was noted in the 1800s in the works of mathematician Carl Friedrich Gauss. The modern understanding was developed by statistician William Sealy Gosset in 1908, though he did not use the term. The term "degrees of freedom" became popular after English biologist Ronald Fisher began using it in 1922 when publishing reports on his work developing chi squares. Degrees of freedom represent the number of values in a study that can vary freely. They are important for understanding chi-square tests and the validity of the null hypothesis.
Measure of Central Tendency (Mean, Median, Mode and Quantiles)Salman Khan
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most values in a distribution fall and are also referred to as the central location of a distribution. You can think of it as the tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method.
- 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.
It is most useful for the students of BBA for the subject of "Data Analysis and Modeling"/
It has covered the content of chapter- Data regression Model
Visit for more on www.ramkumarshah.com.np/
This document discusses various measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. The mean is the average and is calculated by summing all values and dividing by the total number of data points. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently in the data set. Examples are given to demonstrate calculating each measure. The document also discusses advantages and limitations of each central tendency measure.
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
Mean, Median, Mode: Measures of Central Tendency Jan Nah
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found by dividing the sum of all values by the total 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. Each measure provides a single number to represent the central or typical value in a data set.
This document defines and provides instructions for calculating mean, median, mode, and range for a set of numbers. It defines each term, explains the steps to calculate each, and provides examples of calculating mean, median, mode, and range for practice number sets.
This document defines and provides examples for calculating the mean, median, mode, and range of a data set. It explains that the mean is calculated by adding all values and dividing by the number of values, the median involves ordering values and selecting the middle one, the mode is the most frequent value, and the range is the difference between the highest and lowest values. Examples are given for each statistical measure.
This document describes how to characterize the distribution of a quantitative variable in three steps: reporting the center, deviations from the center, and general shape. It discusses various measures of central tendency (mean, median, mode), variation (range, standard deviation, average deviation), and distribution shape (normal curve, skewness). The mean, median, and mode are introduced as measures of central tendency, along with how to calculate each one. Measures of variation like range, standard deviation, and average deviation are also defined and the formulas to compute them provided. Finally, the document discusses the normal distribution curve and how skewness indicates a distribution's departure from symmetry.
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.
Mean, median, mode, Standard deviation for grouped data for Statistical Measu...Renzil D'cruz
Detail Survey on Indian manufacture shampoo for management statistical purpose and calculation of Mean, median, mode, Standard deviation for grouped data for Statistical Measure for Shampoo in Indian market
This document provides an introduction to statistics, including definitions, scope, and measures of central tendency. It defines statistics as the science of collecting, organizing, analyzing, interpreting, and presenting data. Statistics has applications in various fields including social sciences, planning, mathematics, economics, and business management. Common measures of central tendency discussed are the arithmetic mean, geometric mean, harmonic mean, median, and mode. Formulas for calculating the arithmetic mean using individual data, frequency distributions, and class intervals are provided.
The document discusses calculating the mean, median, and mode of data sets. It provides examples of how to calculate the mean by adding all values and dividing by the number of values. The median is found by ordering values and selecting the middle value or averaging the two middle values. The mode is the most frequently occurring value. Examples are given of calculating each measure for various data sets.
This document discusses calculating measures of central tendency (mean, median, mode) from individual series, discrete series, and continuous series data. It provides examples of calculating the mean, median, and mode from various data sets, including individual data points, frequency distributions, and grouped data. The mean is calculated by summing all values and dividing by the total number of data points. The median is found by ordering the data and taking the middle value. The mode is the value that occurs most frequently for individual data and the class with the highest frequency for continuous data.
- Index numbers measure relative changes in variables like prices, quantities, values over time from a base period. They are used to frame policies, reveal trends, and for deflating purposes.
- There are different methods for constructing index numbers, including simple aggregate methods, simple average of relatives methods, and weighted index numbers that assign weights.
- Common weighted indexes include the Laspeyres method which uses base period weights, the Paasche method which uses current period weights, and the Fisher Ideal Index which takes the geometric mean of the Laspeyres and Paasche.
A coffee shop conducted a two-day survey to determine the average number of cappuccinos made per hour. A histogram showed the frequency of cappuccinos made within various hourly intervals. To calculate the average, interval midpoints were determined and multiplied by the frequencies. The total of these products was divided by the total frequency, determining that the average number of cappuccinos made per hour was 10.
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
This document summarizes key concepts from an introduction to statistics textbook. It covers types of data (quantitative, qualitative, levels of measurement), sampling (population, sample, randomization), experimental design (observational studies, experiments, controlling variables), and potential misuses of statistics (bad samples, misleading graphs, distorted percentages). The goal is to illustrate how common sense is needed to properly interpret data and statistics.
The document discusses various measures used to describe the dispersion or variability in a data set. It defines dispersion as the extent to which values in a distribution differ from the average. Several measures of dispersion are described, including range, interquartile range, mean deviation, and standard deviation. The document also discusses measures of relative standing like percentiles and quartiles, and how they can locate the position of observations within a data set. The learning objectives are to understand how to describe variability, compare distributions, describe relative standing, and understand the shape of distributions using these measures.
This document discusses various statistical concepts such as measures of central tendency, measures of dispersion, standard deviation, normal distribution, and tests of significance. It provides examples and formulas to calculate range, mean deviation, standard deviation, z-scores, confidence intervals, and the chi-square test. Biological variation is common and various statistical methods can be used to analyze data and find patterns in large datasets.
This document discusses the normal distribution and related concepts. It begins with an introduction to the normal distribution and its properties. It then covers the probability density function and cumulative distribution function of the normal distribution. The rest of the document discusses key properties like the 68-95-99.7 rule, using the standard normal distribution, and how to determine if a data set follows a normal distribution including using a normal probability plot. Examples are provided throughout to illustrate the concepts.
This document discusses variance and standard deviation. It defines variance as a measure of how data points differ from the mean. It explains that variance can show how two data sets that have the same mean and median can still be different. The document then provides formulas and examples for calculating variance and standard deviation. It states that standard deviation is a measure of variation from the mean and that a higher standard deviation indicates more spread and less consistency in the data.
1) The document discusses standard deviation and variance as measures of how dispersed data points are from the mean. It provides formulas to calculate population variance, sample variance, population standard deviation, and sample standard deviation.
2) Examples are given to demonstrate calculating variance and standard deviation from raw data sets and frequency distributions. This helps determine which data set or person is more consistent.
3) The empirical rule is described, stating that approximately 68%, 95%, and 99.7% of values in a bell-shaped distribution fall within 1, 2, and 3 standard deviations of the mean, respectively.
The document presents information on statistical methods and quality budgeting procedures. It discusses the five steps of quality - say what you do, do what you say, record what you do, review what you do, and restart the process. The budget is divided according to these steps, first describing measures of central tendency like mean, median and mode. It then covers measuring dispersion through tools like range, variance and standard deviation. The document reviews the processes and asks if quality is achieved or not.
This document discusses standard deviation and variance as measures of how data points differ from the mean. It provides formulas for calculating population variance, sample variance, population standard deviation, and sample standard deviation. Examples are shown to demonstrate calculating variance and standard deviation from raw data. The standard deviation measures the average distance of data points from the mean and can indicate how consistently data is clustered around the mean. A lower standard deviation means data is more consistent.
Measures of dispersion describe how spread out or varied the values in a data set are. There are absolute measures like range and interquartile range, and relative measures like coefficient of variation. Range is the difference between the highest and lowest values, while interquartile range describes the middle 50% of values. Mean deviation, variance, and standard deviation are also measures of dispersion that take into account how far values are from the mean or average. Standard error describes the precision of the sample mean as an estimate of the population mean. These measures help determine how representative the central value or mean is of the overall data set.
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
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Chapter 7: Estimating Parameters and Determining Sample Sizes
7.3: Estimating a Population Standard Deviation or Variance
Statistik 1 6 distribusi probabilitas normalSelvin Hadi
This document discusses the key characteristics and concepts of the normal probability distribution. It outlines six goals related to understanding the normal distribution, its properties, calculating z-values, and using the normal distribution to approximate the binomial probability distribution. The key points covered include defining the mean, standard deviation, and shape of the normal curve; transforming variables to the standard normal distribution; and determining probabilities based on the areas under the normal curve.
The document discusses variability and measures of variability. It defines variability as a quantitative measure of how spread out or clustered scores are in a distribution. The standard deviation is introduced as the most commonly used measure of variability, as it takes into account all scores in the distribution and provides the average distance of scores from the mean. Properties of the standard deviation are examined, such as how it does not change when a constant is added to all scores but does change when all scores are multiplied by a constant.
The document discusses four levels of measurement (nominal, ordinal, interval, and ratio) and how they relate to different types of data. It then covers topics in descriptive statistics including frequency distributions, measures of central tendency (mode, median, mean), and measures of dispersion (variance and standard deviation). Key points are that nominal variables use the mode, ordinal variables use the median, and interval/ratio variables use the mean. Variance and standard deviation quantify how spread out values are from the mean.
This document provides an overview of the Student's t-test, which is used to test the significance of differences between two means. It describes unpaired t-tests which compare two independent groups, and paired t-tests which compare two related groups or repeated measures on the same individuals. Two examples of each type of t-test are shown, with step-by-step calculations to test the null hypothesis that the means are not significantly different between groups. The examples conclude whether the differences are statistically significant or could have occurred by chance.
The document provides information about the normal distribution and standard normal distribution. It discusses key properties of the normal distribution including that it is defined by its mean and standard deviation. It also describes the 68-95-99.7 rule for how much of the data falls within 1, 2, and 3 standard deviations of the mean in a normal distribution. The document then introduces the standard normal distribution and how it allows converting any normal distribution to a standard scale for looking up probabilities. It provides examples of calculating probabilities and finding values corresponding to percentiles for both raw and standard normal distributions. Finally, it discusses checking if data are approximately normally distributed.
continuous probability distributions.pptLLOYDARENAS1
The document provides information about the normal distribution and standard normal distribution:
- The normal distribution is defined by its mean (μ) and standard deviation (σ). Changing μ shifts the distribution left or right, while changing σ increases or decreases the spread.
- All normal distributions can be converted to the standard normal distribution (with μ=0 and σ=1) by subtracting the mean and dividing by the standard deviation.
- The standard normal distribution is useful because probability tables and computer programs provide the integral values, avoiding the need to calculate integrals manually.
- For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls
The document discusses measures of central tendency and variability used in statistics. It defines mean, median and mode as the three main measures of central tendency, and how to compute each for both ungrouped and grouped data. For measures of variability, it defines range, variance and standard deviation, and provides examples of computing each for ungrouped and grouped data. The goal is for students to understand and be able to apply these fundamental statistical concepts and calculations.
This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like variables, populations, samples, descriptive statistics, and levels of measurement. It also explains how to calculate measures of central tendency like mean, median, and mode. Additionally, it describes properties of normal and skewed distributions, how to interpret the shape of data, and how to calculate and interpret standard deviation as a measure of variability.
This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like data, variables, parameters, statistics, populations, samples, descriptive statistics, and levels of measurement. It also explains how to calculate measures of central tendency like the mean, mode, and median. Frequency distributions and histograms are presented as ways to summarize and visually depict sample data.
The document discusses family planning objectives such as avoiding unwanted births and regulating birth intervals. It defines eligible couples as currently married couples where the wife is of reproductive age. Target couples are those who have had 2-3 living children. Temporary contraceptive methods include barrier methods like condoms and diaphragms, as well as hormonal methods and IUDs. Permanent methods are also discussed. The document provides details on various contraceptive methods, their effectiveness rates, advantages and disadvantages.
The document discusses various methods for organizing and presenting quantitative and qualitative data, including frequency distribution tables, graphs, charts, and diagrams. It provides examples of different types of tables, bar graphs, pie charts, histograms, line graphs, frequency polygons, scatter plots, and more. It also outlines general principles for designing clear and informative tables, such as using titles, labeling rows and columns, and summarizing the presented data.
Demography and fertility related statistics 2AbhishekDas15
The document discusses various sources of demographic data and methods for population projection. It describes four main sources of demographic data: censuses, vital registration systems, surveys, and sample registration systems. It then outlines four common mathematical methods for population projection: arithmetic growth, geometric growth, exponential growth, and component projection.
This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like variables, populations, samples, descriptive statistics, and levels of measurement. It also explains how to calculate measures of central tendency like mean, median, and mode. Additionally, it describes properties of normal and skewed distributions, how to interpret standard deviation as a measure of variability, and how to calculate standard deviation in Excel.
This document provides an introduction and overview of biostatistics. It defines key biostatistics terms like population, sample, parameter, statistic, quantitative vs. qualitative data, levels of measurement, descriptive vs. inferential biostatistics, and common statistical notations. It also discusses sources of health information and how computerized health management information systems are used to collect, analyze and report data.
This document summarizes guidelines for sterilization procedures and termination of pregnancy in India. It outlines the age requirements for sterilization, which methods are available, and risks/benefits. For termination of pregnancy, it describes the conditions under which abortion is legal in India according to the Medical Termination of Pregnancy Act and rules regarding approval and qualifications of medical practitioners performing the procedure.
How to Download & Install Module From the Odoo App Store in Odoo 17Celine George
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 3)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
Lesson Outcomes:
- students will be able to identify and name various types of ornamental plants commonly used in landscaping and decoration, classifying them based on their characteristics such as foliage, flowering, and growth habits. They will understand the ecological, aesthetic, and economic benefits of ornamental plants, including their roles in improving air quality, providing habitats for wildlife, and enhancing the visual appeal of environments. Additionally, students will demonstrate knowledge of the basic requirements for growing ornamental plants, ensuring they can effectively cultivate and maintain these plants in various settings.
How to stay relevant as a cyber professional: Skills, trends and career paths...Infosec
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As a cybersecurity professional, you need to constantly learn, but what new skills are employers asking for — both now and in the coming years? Join this webinar to learn how to position your career to stay ahead of the latest technology trends, from AI to cloud security to the latest security controls. Then, start future-proofing your career for long-term success.
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Get Success with the Latest UiPath UIPATH-ADPV1 Exam Dumps (V11.02) 2024yarusun
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Artificial Intelligence (AI) has revolutionized the creation of images and videos, enabling the generation of highly realistic and imaginative visual content. Utilizing advanced techniques like Generative Adversarial Networks (GANs) and neural style transfer, AI can transform simple sketches into detailed artwork or blend various styles into unique visual masterpieces. GANs, in particular, function by pitting two neural networks against each other, resulting in the production of remarkably lifelike images. AI's ability to analyze and learn from vast datasets allows it to create visuals that not only mimic human creativity but also push the boundaries of artistic expression, making it a powerful tool in digital media and entertainment industries.
How to Create a Stage or a Pipeline in Odoo 17 CRMCeline George
Using CRM module, we can manage and keep track of all new leads and opportunities in one location. It helps to manage your sales pipeline with customizable stages. In this slide let’s discuss how to create a stage or pipeline inside the CRM module in odoo 17.
10. Skewness Mode = Mean = Median SYMMETRIC Figure 2-13 (b)
11. Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median Figure 2-13 (b) Figure 2-13 (a)
12. Skewness Mode = Mean = Median SKEWED LEFT (negatively ) SYMMETRIC Mean Mode Median SKEWED RIGHT (positively) Mean Mode Median Figure 2-13 (b) Figure 2-13 (a) Figure 2-13 (c)
20. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value)
21. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s
22. Estimation of Standard Deviation Range Rule of Thumb x - 2 s x x + 2 s Range 4 s or (minimum usual value) (maximum usual value) Range 4 s = highest value - lowest value 4
23.
24.
25.
26. x The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
27. x - s x x + s 68% within 1 standard deviation 34% 34% The Empirical Rule (applies to bell-shaped distributions ) FIGURE 2-15
28. x - 2s x - s x x + 2s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations The Empirical Rule (applies to bell-shaped distributions ) 13.5% 13.5% FIGURE 2-15
29. x - 3s x - 2s x - s x x + 2s x + 3s x + s 68% within 1 standard deviation 34% 34% 95% within 2 standard deviations 99.7% of data are within 3 standard deviations of the mean The Empirical Rule (applies to bell-shaped distributions ) 0.1% 2.4% 2.4% 13.5% 13.5% FIGURE 2-15 0.1%
Editor's Notes
page 58 of text Name the two values if the set is bimodal
Data skewed to the left is said to be ‘negatively skewed’ with the mean and median to the left of the mode. Data skewed to the right is said to be ‘positively skewed’ with the mean and media to the right of the mode.
Data not ‘lopsided’.
Data lopsided to left (or slants down to the left - definition of skew is ‘slanting’)
Data lopsided to the right (or slants down to the right)
Reminder: range is the highest score minus the lowest score
Reminder: range is the highest score minus the lowest score
Reminder: range is the highest score minus the lowest score
These ideas will be used repeatedly throughout the course.
page 79 of text
Some student have difficulty understand the idea of ‘within one standard deviation of the mean’. Emphasize that this means the interval from one standard deviation below the mean to one standard deviation above the mean.
These percentages will be verified by the concepts learned in Chapter 5. Emphasize the Empirical Rule is appropriate for data that is in a BELL-SHAPED distribution.
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