Statistics For Data Science | Statistics Using R Programming Language | Hypothesis Testing | Edureka

Introduction to Statistics
Terminology
Categories in Statistics
Descriptive & Inferential
Statistics
Statistics in R
Descriptive Statistics in R
Inferential Statistics in R
Agenda

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Statistics is a branch of mathematics dealing with data collection and organization, analysis,
interpretation and presentation.

Analyse Data
Build a Model
Infer Result

Statistics
Stock
Market
Life
Sciences
Weather
Retail
Insurance
Education

Basic Terminology
There are a few statistical terms one should be aware of while dealing with statistics.
Population ParameterSample Variable

Basic Terminology
Population is the set of sources from which data has to be
collected.

Basic Terminology
A Sample is a subset of the Population.

Basic Terminology
A variable is any characteristics, number, or quantity that can
be measured or counted.
A variable may also be called a data item.
Gender Age Region
Height
Weight
Income
Blood Group Ethnicity
Degree
Time
Language

Basic Terminology
Also known as a statistical model, A statistical
Parameter or population parameter is a quantity that
indexes a family of probability distributions.
µ
∑
х

Types of Analysis
An analysis can be done in one of two ways.
Analysis
Quantitative Qualitative

Types of Analysis
An analysis can be done in one of two ways.
Also known as Statistical Analysis,
it is the science of collecting &
interpreting objects with numbers.
Also known as Non-statistical
Analysis, it mostly deals with
generic data using text, media, etc
Analysis
Quantitative Qualitative

Inferential statistics makes inferences and predictions about a
population based on a sample of data taken from the population in
question.
Descriptive statistics uses the data to provide descriptions of the
population, either through numerical calculations or graphs or
tables.
Categories in Statistics
There are two major categories in Statistics.
Descriptive
InferentialInferential

Descriptive Statistics
This method, is mainly focused upon the main characteristics of data. It provides graphical
summary of the data.
Characteristics of Data

Maximum
Minimum
Average
This method, is mainly focused upon the main characteristics of data. It provides graphical
summary of the data.

Inferential Statistics
This method, generalizes a large dataset and applies probability to draw a conclusion. It allows us
to infer data parameters based on a statistical model using a sample data.
Statistical Model
Start
Process Step
Decision
Answer
Choice I
Choice II

Tall
Short
Average
This method, generalizes a large dataset and applies probability to draw a conclusion. It allows us
to infer data parameters based on a statistical model using a sample data.

Descriptive Statistics – Statistical Measures

Descriptive Statistics – Use Case
Here is a sample dataset of cars containing
the variables: Cars, Mileage per
Gallon(mpg), Cylinder Type (cyl),
Displacement (disp), Horse Power(hp) &
Real Axle Ratio(drat).
Using descriptive Analysis, you can analyse
each of the variables in the dataset for
mean, standard deviation, minimum and
maximum.
Cars mpg cyl disp hp drat
A 21 6 160 110 3.9
B 21 6 160 110 3.9
C 22.8 4 108 93 3.85
D 21.3 6 108 96 3
E 23 4 150 90 4
F 23 6 108 110 3.9
G 23 4 160 110 3.9
H 23 6 160 110 3.9

Measures of the Centre
Mean Median Mode

If we want to find out the average
horsepower of the cars among the
population of cars, we will check and
calculate the average of all values. In this
case,
A 21 6 160 110 3.9
B 21 6 160 110 3.9
C 22.8 4 108 93 3.85
D 21.3 6 108 96 3
E 23 4 150 90 4
F 23 6 108 110 3.9
G 23 4 160 110 3.9
H 23 6 160 110 3.9
110 + 110 + 93 + 96 + 90 + 110 + 110 + 110
8
= 103.625

Mean Median Mode
Measure of average of all the values in a sample is called Mean.

If we want to find out the centre value of
mpg among the population of cars, we will
arrange the mpg values in ascending order
to choose the middle value. In this case,
21,21,21.3,22.8,23,23,23,23
But in case of even entries, we take
average of the two middle values. In this
case,
22.8+23
2
= 22.9
A 21 6 160 110 3.9
B 21 6 160 110 3.9
C 22.8 4 108 93 3.85
D 21.3 6 108 96 3
E 23 4 150 90 4
F 23 6 108 110 3.9
G 23 4 160 110 3.9
H 23 6 160 110 3.9

Mean Median Mode
Measure of the central value of the sample set is called Median.

If we want to find out the most common
type of cylinder among the population of
cars, we will check the value which is
repeated most number of times.
4 6
4 6
A 21 6 160 110 3.9
B 21 6 160 110 3.9
C 22.8 4 108 93 3.85
D 21.3 6 108 96 3
E 23 4 150 90 4
F 23 6 108 110 3.9
G 23 4 160 110 3.9
H 23 6 160 110 3.9

Mean Median Mode
The value most recurrent in the sample set is known as Mode.

Measures of the Spread
Range Standard DeviationInter Quartile Range Variance

Measures of Spread
Range is the given measure of how spread apart the values in a dataset are.
Range = Max(𝑥𝑖) - Min(𝑥𝑖)

Measures of Spread
Inter Quartile Range(IQR) is the measure of variability, based on dividing a dataset into
quartiles.
1 2 3 4 5 6 7 8

Measures of Spread
Quartile
1 2 3 4 5 6 7 8
Q1 Q2 Q3

Measures of Spread
Quartile
1 2 3 4 5 6 7 8
Q1 Q2 Q3
Q1=
2+3
2
=2.5

Measures of Spread
Quartile
1 2 3 4 5 6 7 8
Q1 Q2 Q3
Q2=
4+5
2
=4.5

Measures of Spread
Quartile
1 2 3 4 5 6 7 8
Q1 Q2 Q3
Q3=
6+7
2
=6.5

Measures of Spread
Inter Quartile Range
1 2 3 4 5 6 7 8
Q1 Q3

Measures of Spread
Variance describes how much a random variable differs from its expected value.
It entails computing squares of deviations.

Measures of Spread
❖ Deviation is the difference between each element from the mean.
Deviation = (𝑥𝑖-µ)

Measures of Spread
❖ Population Variance is the average of squared deviations.
σ² = ෍
𝑖=1
𝑁
= (𝑥𝑖−𝜇)²
1
𝑁

Measures of Spread
❖ Sample Variance is the average of squared differences from the mean.
s² = ෍
𝑖=1
𝑁
= (𝑥𝑖− ҧ𝑥)²
1
(𝑛 − 1)

Measures of Spread
Standard Deviation is the measure of the dispersion of a set of data from its mean.
σ = ෍
𝑖=1
𝑁
= (𝑥𝑖−𝜇)²
1
𝑁

Standard Deviation– Use Case
Ross has 20 Dinosaur figures. They have the numbers 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4,
10, 9, 6, 9, 4. Work out the Standard Deviation.
Find out the
mean for your
sample set.
STEP 1 The Mean is:
9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4
20
⸫µ=7

Then for each
number, subtract
the Mean and
square the result.
STEP 2
(𝑥𝑖−𝜇)²
(9-7)²= 2²=4
(2-7)²= (-5)²=25
(5-7)²= (-2)²=4
And so on…
⸫ We get the following results:
4, 25, 4, 9, 25, 0, 1, 16, 4, 16, 0, 9, 25, 4, 9, 9, 4, 1, 4, 9

Then work out the
mean of those
squared
differences.
STEP 3 ෍
𝑖=1
𝑁
= (𝑥𝑖−𝜇)²
1
𝑁
4+25+4+9+25+0+1+16+4+16+0+9+25+4+9+9+4+1+4+9
20
⸫ σ² = 8.9

Take square root
of σ².
STEP 4
⸫ σ = 2.983
෍
𝑖=1
𝑁
= (𝑥𝑖−𝜇)²
1
𝑁
σ =

Statistics in R
❖ R is open-source and freely available.
❖ R is cross-platform compatible.
❖ R is a powerful scripting language.
❖ R is highly flexible and evolved.
Reasons for moving to R

Inferential Statistics – Hypothesis Testing

Hypothesis Testing
Statisticians use hypothesis testing to formally check whether the hypothesis is accepted or
rejected.
Hypothesis testing is conducted in the following manner:
❖ State the Hypotheses – This stage involves stating the null and alternative hypotheses.
❖ Formulate an Analysis Plan – This stage involves the construction of an analysis plan.
❖ Analyse Sample Data – This stage involves the calculation and interpretation of the test
statistic as described in the analysis plan.
❖ Interpret Results – This stage involves the application of the decision rule described in the
analysis plan.

Hypothesis Testing
Nick John Bob Harry
Assume the event is free of bias.
So, what is the probability of John not cheating?

Hypothesis Testing
Nick John Bob Harry
P(John not picked for a day) =
3
4
P(John not picked for 3 days) =
3
4
×
3
4
×
3
4
= 0.42 (approx)
P(John not picked for 12 days) = (
3
4
) 12
= 0.032 < 𝟎. 𝟎𝟓

Hypothesis Testing
Nick John Bob Harry
Null Hypothesis (𝑯 𝟎) : Result is no different from assumption.
Alternate Hypothesis (𝑯 𝒂) : Result disproves the assumption.
Probability of Event < 𝟎. 𝟎𝟓 (5%)

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