A_Movie_Review_Pursuit_Of_Happy

1. 7/19/2020 1

2. Educational Statistics
Lecture No. 5.
Measures of Central Tendency
2

3. Learning Objectives
After completion of unit, the students will be able to:
1. Write down the goals of measure of centraltendency.
2. Explain the characteristics of central tendency.
3. Determine mean and merits and demerits of mean.
4. Define median, its merits and calculation.
5. Explain Mode, merits, demerits and calculation.
6. Write Measures of Dispersion, merits and demerits.
7. Calculate the Measures of Dispe7r
/19s
/202
i
0 on.
3

4. Descriptive Statistics
Descriptive
Statistics
Measures of
Central
Tendency
Measures of
Dispersion
4

5. Measures of Central tendency
Measures of Central
Tendency
Mean Mode
Median
Geometric
Mean
Harmonic
Mean
5

6. Measures of Central tendency
VIDEO
https://youtu.be/179ce7ZzFA8

7. Measures of Central tendency
Introduction
An average is a single value, which represents the set of data as whole.
Since the average tends to lie in the center of distribution they are also
called measure of central tendency. There are three methods of measuring
the center of any data.
Arithmetic mean
The Median
The Mode
7

8. Measures of Central tendency
The goal of the measure of central tendency is:
i) Tocondense data in a single value.
ii) Tofacilitate comparison between data.
Commonly used measures of central tendency are the
mean, the median and the mode.
Each of these indices is used with a different scale of
measurement.
8

9. Mean orAverage
Arithmetic Mean
It is defined as the sum of all the observations divided by
the number of observations. It is denoted by X.
When to use ArithmeticMean
Weuse arithmetic mean, when we are required to study
social, economic and commercial problems like
production, price, export and import. It helps in getting
average income, average price, average pro
9
duction etc.

10. Example of Mean
The formula for computing the mean is:
(Mean score) X = ƩX/n
Where Ʃ represents “Sum of”, X represents anyraw score
value, n represents total number of scores. Example:
5, 10, 12, 16, 8, 42, 25, 15, 10,7
Solution: 5+10+12+16+8+42+25+15+10+7=150/10
 Mean = 15

11. Interpretation of Mean
To interpret the as the “balance point or the center value”, we can
use the analogy of a seesaw. Its mean lies right at the center where
the fulcrum keeps the board perfectly balanced. As the mean is
based on every score or value of the dataset so it is influenced by
outliers and skewed distribution.
7/19/2020 11

12. Mean orAverage
12
Qualities of GoodAverage
An average that possesses all or most of the following qualities is
considered good average.
It should be rigidly defined.
It should be easy to understand and easy to calculate.
It should be based on all the observations of the data.
It should be unaffected by extreme observations.
It should have sampling stability

13. Advantages of Mean
13
Qualities of GoodAverage
An average that possesses all or most of the following qualities is
considered good average.
It should be rigidly defined and easy to understand.
It should be easy to calculate.
It should be based on all the observations of the data.
It should be unaffected by extreme observations.
It should have sampling stability

14. Disadvantages of Mean
14
It is highly affected by extreme values.
It cannot be accurately calculated for openend
frequency distribution.
It cannot be calculated accurately if any observationis
missing.
It can not be located graphically.

15. Median
Median is the middle most value of a set of data when the data is
arranged in order of magnitude. If the number of observations is
in odd form, then median is the mid value and if the number of
observations is even form, then median is the average of two
middle values.
When we ApplyMedian
We apply median to the situations, when the direct measurements
of variables are not possible like poverty,beauty and intelligence
etc.

16. Example Median
Median
Example: 12,15, 10, 20, 18, 25, 45, 30, 26
We need to make order of the data
10, 12, 15, 18, 20, 25, 26, 30, 45

So Median = 20
16

17. Advantages Median
17
It is easy to calculate and understand.
It is not affected by extreme values.
It can be computed even in open end frequency
distribution.
It can be used for qualitative data.
It can be located graphically.

18. Disadvantages Median
18
Disadvantages of Median
It is not rigorously defined.
It is not based on all the observations.
It is not suitable for further algebraic treatment.

19. Mode
7/19/2020 19
The most frequent value that occurs in the set of data is called
mode.Aset of data may have more than one mode or nomode.
When it has one mode it is called uni-modal. When it has two
or three modes it is called bi-modal or tri-modal respectively.
Example
12, 24, 15, 18, 30, 48, 20, 24
So Mode = 24

20. Application of Mode
7/19/2020 20
When to apply Mode
We apply mode when it is required to study the
problems like average size of shoes, average size
of readymade garments, and average size of
agriculture holding. This average is widely used in
Biology and Meteorology.

21. Advantages of Mode
7/19/2020 21
It is easy to understand.
It is not affected by extreme values.
It can be computed even in open-end classes.
It can be useful in qualitative data.


22. Disadvantages of Mode
7/19/2020 22
It is not clearly defined.
It is not suitable for further algebraic treatment.
It is not based on all the observations.
It may not exist in some cases.

23. Assessment
7/19/2020 23
Calculate the following.
1.Alist of five test scores was 60, 67, 73, 63and
67. Find the following:
a) Mean
b) Median
c) Mode

24. Measures of Dispersion
Measures of
Dispersion
Range
Interquartile
Range
Standard
Deviation
Quartile
Deviation
V
ariance
7/19/2020 24

25. Measures of Dispersion
7/19/2020 25
The measure of central tendency does not tell us anything
about the spread data because any two sets of data may
have same central tendency with vast difference magnitude
of variability. Consider two types of data sets have same
mean but different reliability.
10, 12, 11, 14, 13
10, 2, 18, 27, 3

26. Measures of Dispersion
• These two data have same mean 12, but differ in their
variations. There is more variation in data (b) as compared to
data (a).
• This illustrates the fact that of central tendency is not sufficient.
• Wetherefore need some additional information concerning with
how the data are dispersed about the average.
• This is measuring the dispersion.
• By dispersion we mean the degree to which data tend to spread
about an average value.
• There are two types of measures of dispersion, absolute and
relative dispersion.
7/19/2020 26

27. Types Measures of Dispersion
Measures of Dispersion
Followings are the measure of dispersion.
The Range
The semi Interquartile Range or the Quartile Deviation
The Mean Deviation
The variance and the standard deviation
27

28. Range
It is defined as difference between largest and smallest
observations in a set of data. Range = R = Xm -X0
Where Xm = the largest observation X0 = the smallest
observation. The range is very simple measure of
variability and only concerned with two most extreme
observations. Its relative measure is known as the co-
efficient of dispersion. Xm - Xo
Co-efficient of Range = Xm + Xo 28

29. Example of Range
Example:
Calculate Range and Co-efficient of Range fromthe following
data. 15, 20, 18, 16, 30, 42, 12,25
Solution:
Xm = 42, Xo = 12 R = Xm — Xo =42-12 =30

29

30. Standard Deviation
 Standard deviation is the most commonly used and the most
important measure of variation.
 It determines whether the scores are generally near orfar from
the mean.
 In simple words, standard deviation tells how tightly allthe
scores are clustered around the mean in a data set.
 When the scores are close to the mean, standard deviation is small.
And large standard deviation tells thatthe
scores are spread apart. Standard devi
7/
a
19/t
202
i
0on is s
30 imply square
root of variance

31. Variance
• Variance (σ2) in statistics is a measurement of the
spread between numbers in a data set.
• That is, it measures how far each number in the set
is from the mean and therefore from every other
number in the set.
• Variance measures how far a data set is spread out.
• Itis mathematically defined as the average of the
squared differences from the mean.
31

32. Normal Curve
One way of presenting out how data are distributed isto plot them in a
graph.
If the data is evenly distributed, our graph will come
across a curve.
In statistics this curve is called a normal curve and in social
sciences, it is called the bell curve.
Normal or bell curved is distribution of data may
naturally occur in several possible ways, with a number of possibilities
for standard deviation

33. Standard Normal Curve

7/19/2020 33

34. Skewness
7/19/2020 34
Skewness tells us about the amount and direction of the variation of
the data set.
It is a measure of symmetry.Adistribution or data setis
symmetric if it looks the same to the left and right of the central
point.
If bulk of data is at the left i.e. the peak is towards left
and the right tail is longer, we say that the distribution is skewed
right or positively skewed.

35. Examples of Skewness
7/19/2020 35

36. Kurtosis
36
 Kurtosis is a parameter that describes the shape of variation.It is a
measurement that tells us how the graph of the set of data is
peaked and how high the graph is around the mean.
 In other words we can say that kurtosis measures the shape of
the distribution, .i.e. the fatness of the tails, it focuses on how
returns are arranged around the mean.
 A positive value means that too little data is in the tail and
positive value means that too much data is in the tail.

37. Types of Kurtosis
Kurtosis has three types, mesokurtic, platykurtic, and
leptokurtic.
If the distribution has kurtosis of zero, then the graph is
nearly normal. This nearly normal distribution is called
mesokurtic.
If the distribution has negative kurtosis, it is called
platykurtic. An example of platykurtic distribution isa
uniform distribution.
 If the distribution has positive kurtosis, it is called
leptokurtic
37

38. Types of Kurtosis
7/19/2020 38

39. Self AssessmentActivity
Q. 1. Tell the basic purpose of measure of central tendency?
Q. 2. Define Range and determine range of a given data?
Q. 3. Write down the formulas for determining quartiles?
Q. 4. Define mean or average deviation?
Q. 5. Determine variance and standard deviation?
Q. 6. Define normal curve?
Q. 7. Explain skewness and kurtosis?
Q. 8. Define dispersion, its types, merits, demerits and
Applications.
39

40. 7/19/2020 40