If everything were the same, we would have no need of statistics. But, people's heights, ages, etc., do vary. We often need to measure the extent to which scores in a dataset differ from each other. Such a measure is called the dispersion of a distribution.

1. Welcome
To The
Presentation

2. Presentation
Statistics
STA-240
Instructor
Mohammad Mortuza Ahmmed
2

3. GROUP NAME
F
Our Presentation Topic:
“Measures of Dispersion”

4. Group Members
Hussain
Mohammad
Jakaria
ID#12206018
Md. Shakik
Zunaed
ID#12206004
Md. Shariful
Haque Robin
ID#12206049
Md. Hassan
Shahriar
ID#12206013

5. MEASURES OF DISPERSION
If everything were the same, we would have no
need of statistics. But, people's heights, ages, etc.,
do vary. We often need to measure the extent
to which scores in a dataset differ from each
other. Such a measure is called the dispersion of
a distribution.

6. • To know the average variation of different
values from the average of a series
• To know the range of values
• To compare between two or more series
expressed in different units
• To know whether the Central Tendency truly
represent the series or not

7. Types of Measures of Dispersion
MEASURES
OF
DISPERSION
Range (R)
Mean Deviation
(MD)
Variance
Standard Deviation
(SD)

8. Range
The range is the difference between the
highest and lowest values of a dataset.
Example : For the dataset {4, 6, 9, 3, 7} the
lowest value is 3, highest is 9, so the range is
9-3=6.

9. Mean Deviation
• The mean deviation is the mean of the
absolute deviations of a set of data about
the mean. For a sample size N, the mean
deviation is defined by

10. Example :
Saddam took five exams in a class and had scores of 92, 75, 95, 90, and 98.
Find the mean
deviation for his test scores.
We can say that on the average, Saddam’s test scores deviated by 6 points from the mean.

11. Variance
The variance (σ2) is a measure of how far each
value in the data set is from the mean.

12. Standard Deviation
Standard Deviation it is the square root of the
Variance defined as

13. Example: Saddam took ten exams in STA 240 and had scores of
44, 50, 38, 96, 42, 47, 40,
39, 46, and 50. Find the variance for his test scores.
Mean = (44 + 50 +38 +96 + 42 +47 +40+ 39 + 46+ 50) / 10 = 49.2

14. Example For the above example: Standard
Deviation, σ = √ 260.04 = 16.12. We can say
that on the average, Saddam’s test scores vary
by 16.12 points from the mean. Standard
Deviation is the most important, reliable,
widely used measure of dispersion. It is the
most flexible in terms of variety of
applications of all measures of variation. It is
used in many other statistical operations
like sampling techniques, correlation and
regression analysis, finding co-efficient of
variation, skewness, kurtosis, etc.

15. Coefficient of Variation
The coefficient of variation (CV) is defined as the
ratio of the standard deviation to the mean :
Cv = Standard Deviation / Mean
CV should be computed only for data measured on
a ratio scale. It may not have any
meaning for data on an interval scale.

16. Why Coefficient of Variation
The coefficient of variation (CV) is used to
compare different sets of data having the units
of measurement. The wages of workers may be
in dollars and the consumption of meat in their
families may be in kilograms. The standard
deviation of wages in dollars cannot be
compared with the standard deviation of
amounts of meat in kilograms. Both the
standard deviations need to be converted into
coefficient of variation for comparison. Suppose
the value of CV for wages is 10% and the value
of CV for kilograms of meat is25%. This means
that the wages of workers are consistent.

17. 17
THANK YOU
TO ALL…

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