Business statistics (Basics)

Basics of Statistics
Definition: Science of collection, presentation, analysis, and
reasonable interpretation of data.
Statistics presents a rigorous scientific method for gaining insight into
data.
For example, suppose we measure the weight of 100 patients in a
study.
With so many measurements, simply looking at the data fails to
provide an informative account.
However statistics can give an instant overall picture of data based on
graphical presentation or numerical summarization irrespective to the
number of data points.
Besides data summarization, another important task of statistics is to
make inference and predict relations of variables.
1

Data
 The measurements obtained in a
research study are called the data.
 The goal of statistics is to help
researchers organize and interpret
the data.
2

 Descriptive statistics are methods for
organizing and summarizing data.
 For example, tables or graphs are used to
organize data, and descriptive values
such as the average score are used to
summarize data.
 A descriptive value for a population is
called a parameter and a descriptive
value for a sample is called a statistic.
Descriptive Statistics
3

DataAnalysis
From Data Analysis to
Inference
Population
Samples
Collect data from a
representative
Sample...
Perform Data
Analysis, keeping
probability in mind…
Make an Inference
about the Population.
6

Inferential statistics are methods for using
sample data to make general conclusions
(inferences) about populations.
Because a sample is typically only a part of the
whole population, sample data provide only
limited information about the population.
As a result, sample statistics are generally
imperfect representatives of the corresponding
population parameters.
7

 The discrepancy between a sample
statistic and its population parameter
is called sampling error.
 Defining and measuring sampling error
is a large part of inferential statistics.
Sampling Error
8

Statistical Description of Data:
Descriptive Statistics
 Statistics describes a numeric set of
data by its
 Center
 Variability
 Shape
 Statistics describes a categorical set
of data by
 Frequency, percentage or proportion of
each category
10

Variable
 A variable is a characteristic or condition that
can change or take on different values.
Or any characteristic of an individual or an entity
 Most research begins with a general question
about the relationship between two variables
for a specific group of individuals.
11

Variable -. Variables can be categorical(Discrete) or
quantitative(Discrete and continuous) .
Categorical Variables
• Nominal - Categorical variables with no inherent order or
ranking sequence such as names or classes (e.g., gender,
blood group). Value may be a numerical, but without
numerical value (e.g., I, II, III). The only operation that can
be applied to Nominal variables is enumeration (counts).
• Ordinal - Variables with an inherent rank or order,
e.g. mild, moderate, severe. Can be compared for equality, or
greater or less, but not how much greater or less. mild,
moderate or severe illness). Often ordinal variables are re-
coded to be quantitative.
12

Interval - Values of the variable are ordered as in
Ordinal, and additionally, differences between values
are meaningful, however, the scale is not absolutely
anchored.
Calendar dates and temperatures on the Fahrenheit
scale are examples Addition and subtraction, but not
multiplication and division are meaningful operations.
Ratio - Variables with all properties of Interval plus an
absolute, non-arbitrary zero point, e.g. age, weight,
temperature (Kelvin). Addition, subtraction,
multiplication, and division are all meaningful
operations.
Variables (Contd)
13

Distribution
Distribution - (of a variable) tells us what values
the variable takes and how often it takes these
values.
• Unimodal - having a single peak
• Bimodal - having two distinct peaks
• Symmetric - left and right half are mirror
images.
14

Frequency Distribution
Age 1 2 3 4 5 6
Frequency 5 3 7 5 4 2
Frequency Distribution of Age
Grouped Frequency Distribution of Age:
Age Group 1-2 3-4 5-6
Frequency 8 12 6
Consider a data set of 26 children of ages 1-6 years. Then the
frequency distribution of variable ‘age’ can be tabulated as
follows:
15

Cumulative Frequency
Age Group 1-2 3-4 5-6
Frequency 8 12 6
Cumulative Frequency 8 20 26
Age 1 2 3 4 5 6
Frequency 5 3 7 5 4 2
Cumulative Frequency 5 8 15 20 24 26
Cumulative frequency of data in previous slide
16

Data Presentation
Two types of statistical presentation of data –
Graphical Presentation and Numerical Presentation
Graphical Presentation: We look for the overall pattern and for
striking deviations from that pattern. Over all pattern usually
described by shape, center, and spread of the data.
An individual value that falls outside the overall pattern is called
an Outlier.
Bar diagram and Pie charts - Categorical data.
Two Way Table and Conditional Distribution
Histogram, Stem and Leaf Plot, Box-plot
are used for numerical variable presentation.
17

Data Presentation –Categorical
Variable
Bar Diagram: Lists the categories and presents the percent or count of
individuals who fall in each category.
Eye Color Frequency/
No
of
Obje
cts
Proportion Percent
(%)
1 15 (15/60)=0.25 25.0
2 25 (25/60)=0.333 41.7
3 20 (20/60)=0.417 33.3
Total 60 1.00 100
0
5
10
15
20
25
30
1 2 3
NumberofSubjects
Eye Color
Figure 1:Bar Chart of Subjects in
Treatment Groups
18

Data Presentation –Categorical
Variable
Pie Chart: Lists the categories and presents the percent or count of
individuals who fall in each category.
Figure 2: Pie Chart of
Subjects in Treatment Groups
25%
42%
33% 1
2
3
Color of
Eye
Frequency Proportion Percent
(%)
1 15 (15/60)=0.25 25.0
2 25 (25/60)=0.333 41.7
3 20 (20/60)=0.417 33.3
Total 60 1.00 100
19

Graphical Presentation –Numerical
Variable
Figure 3: Age Distribution
0
2
4
6
8
10
12
14
16
40 60 80 100 120 140 More
Age in Month
NumberofSubjects
Histogram: Overall pattern can be described by its Shape, Center,
and Spread.
The following age distribution is right skewed. The center lies
between 80 to 100. No outliers.
Mean 90.41666667
Standard Error 3.902649518
Median 84
Mode 84
Standard Deviation 30.22979318
Sample Variance 913.8403955
Kurtosis -1.183899591
Skewness 0.389872725
Range 95
Minimum 48
Maximum 143
Sum 5425
Count 60
20

Graphical Presentation –Numerical
Variable
Box-Plot: Describes the Five-Number Summary
0
20
40
60
80
100
120
140
160
1
q1
min
median
max
q3
Figure 3: Distribution of Age
Box Plot
21

Business statistics (Basics)

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