This pused to find measures of dispersion.pt tells us what dispersion is, need of dispersion and the different methods

1. THE MEASURES OF DISPERSION :
AGRICULTURAL PRODUCTION FOODGRAINS
Made By :
Mohit Mahajan
MBA-IB ( 13 )
Submitted to : Dr. Dilip Raina

2. WHY STUDY DISPERSION ???
An average, such as the mean
or the median only locates the
center of the data.
An average does not tell us
anything about the spread of the
data.

3. WHAT IS DISPERSION ?
Dispersion ( also known as
Scatter , spread or variation )
measures the items vary from
some central value.
It measures the degree of
variation.

4. SIGNIFICANCE OF MEASURING
DISPERSION :
To determine the reliability of an
average.
To facilitate comparison.
To facilitate control.
To facilitate the use of other
statistical measures.

5. PROPERTIES OF GOOD MEASURES OF
DISPERSION :
Simple to understand and easy to
calculate.
Rigidly defined.
Based on all items.
A meanable to algebric treatment.
Sampling stability.
Not unduly affected by extreme items.

6. Absolute
measure of
dispersion
Based on
Selected
Items
Range
Inter
Quartile
Range
Based on
all Items
Mean
deviation
Standard
deviation

7. Relative measure of
Dispersion
Based on
Selective Items
Coefficient
of range
Coefficient
of QD
Based on all Items
Coefficient
of MD
Coefficient
of SD
Coefficient
of Variation

8. A small value for a measure of
dispersion indicates that the data are
clustered closed ( the mean is
therefore the representative of the
data ).
A large measure of dispersion
indicates that the mean is not reliable(
it is not the representative of the data).

10. METHODS OF STUDYING VARIATION :
 The Range
 The Inter Quartile Range and the Quartile Deviation
 Mean Deviation
 Standard Deviation

11. THE RANGE
 The simplest measure of dispersion is the range.
 Foe ungrouped data , the range is the difference
between the highest and the lowest value in a set of
data.
RANGE = HIGHEST VALUE – LOWEST VALUE

12. RANGE
Rice Wheat Cereals Pulses Total
81.12 87.86 30.324 10.90 200.73

13. COEFFICIENT OF RANGE :
 Coefficient of Range is calculated as ,
Coefficient of Range= L-S
L+S

14. COEFFICIENT OF RANGE
Rice Wheat Cereals Pulses Total
0.613 0.846 0.343 0.392 0.609

15. MERITS OF RANGE
Simple to understand and the
easiest to compute.
Takes less time to calculate.
It does not require any special
knowledge.

16. LIMITATIONS OF RANGE :
 Range is not based on each and every item
of distribution.
 It takes in to account only the most extreme
values.
 Range can not computed be in case of open
end distribution.
 It does not indicate the direction of
variability.

17. INTERQUARTILE RANGE
 It is the second measure of dispersion, no doubt
improved version over the range.
 It is based on the quartiles so while calculating this
may require upper quartile (Q3) and lower quartile
(Q1) .
 It is the deference between two quartiles
Interquartile range = Q3 – Q1

19. INTER QUARTILE RANGE :
Rice Wheat Cereals Pulses Total
Q1 = 40.82
Q3 = 84.51
43.71
Q1 = 23.89
Q3 = 69.35
45.453
Q1 = 26.08
Q3 = 33.52
7.442
Q1 = 11.39
Q3 = 13.84
2.448
Q1 = 99.83
Q3 = 199.43
99.6

20. COEFFICIENT OF QUARTILE DEVIATION
 Quartile Deviation = Q3 – Q1
Q3 + Q1
Rice Wheat Cereals Pulses Total
Q1 = 40.82
Q3 = 84.51
0.348
Q1 = 23.89
Q3 = 69.35
0.487
Q1 = 26.08
Q3 = 33.52
0.124
Q1 = 11.39
Q3 = 13.84
0.0969
Q1 = 99.83
Q3 = 199.43
0.332

21. MERITS OF QUARTILE DEVIATION:
 It can be easily calculated and simply understood.
 It does not involve much mathematical difficulties.
 As it takes middle 50% terms hence it is a measure
better than Range and Percentile Range.
 It is not affected by extreme terms as 25% of upper
and 25% of lower terms are left out

22. LIMITATIONS OF QUARTILE DEVIATION
It is not suited to algebraic treatment.
It is very much affected by sampling
fluctuations.
The method of Dispersion is not based
on all the items of the series.
It ignores the 50% of the distribution.

23. MEAN DEVIATION :
 The mean deviation takes into consideration all of
the values.
 Mean Deviation : The arithmetic mean of the
absolute values of the deviations from the
arithmetic mean
x= value of each observation
x= the arithmetic mean of the
values
n = the no of observations.

24. MEAN DEVIATION :
Rice Wheat Cereals Pulses Total
21.76 23.14 4.44 1.71 50.26

25. MERITS OF MEAN DEVIATION
It is easy to understand
It is based on all the items of the
series.
It is less affected by extreme values.
It is useful in small samples when no
detailed analysis is required

26. LIMITATIONS OF MEAN DEVIATION
 It lack properties such that ( + ) and ( - )
signs which are not taken in to
consideration.
 It is not suitable for mathematical treatment.
 It may not give accurate results when the
degree of variability in a series is very high.

27. STANDARD DEVIATION
 Standard deviation is the most commonly
used measure of dispersion.
 Similar to the mean deviation , the standard
deviation takes in to account the value of
every observation.
 The values of the mean deviation and the
standard should be relatively similar.
 It is a measure of spread of data about the
mean. SD is the square root of sum of
squared deviation from the mean divided by
the number of observations.

28. STANDARD DEVIATION :
Rice Wheat Cereals Pulses Total
24.43 26.69 5.71 61.48 57.77

29. PROPERTIES OF STANDARD DEVIATION
Independent of change of origin.
Not independent of change of scale.
Fixed relationship among measures of
Dispersion.

30. MERITS OF STANDARD DEVIATION :
 It is based on all the items of the distribution.
 It is meanable to algebraic treatment since actual +
or – signs deviations are taken into consideration.
 It is least affected by fluctuations of sampling.
 It provides a unit of measurement for the normal
distribution.

31. LIMITATIONS OF STANDARD DEVIATION :
 It can’t be used for comparing the variability
of two or more series of observations given
in different units.
 It is difficult to compute and compared.
 It is very much affected by the extreme
values.
 The standard deviation can not be
computed for a distribution with open end
classes.

32. THANK YOU