Introduction of Dispersion, measures, ranges, quartile deviation, mean deviation, standard deviation,

1. Presented By:-
Deepanshu Goyal
Devendra Singh
Rathore
Md. Ibrahim Azaz
Meghna Sharma
Presented to:-
Prof. Rajesh Gupta

2. INTRODUCTION OF
DISPERSION
An average is a single value which
represents a set of values in a distribution.
It is the central value which typically
represents the entire distribution.
Dispersion, on the other hand, indicates
the extend to which the individual value fall
away from the average or a the central
value. This measure brings out how to
distribution with the same average value
may have wide differences in the spread of
individual values around the central value.

3. DEFINITION
“Dispersion is the measure of variations of
the items”.
- A.E.
Bowley
“Dispersion or spread is the degree of the
scatter or variation of the variable about a
central value”.
- Brooks & Dick

4. MEASURES OF
DISPERSION
 Absolute Measure
◦ Range
◦ Quartile Deviation
◦ Mean Deviation
◦ Standard Deviation
 Relative Measure
◦ Co-Efficient of Range
◦ Co-Efficient of Quartile
Deviation
◦ Co-Efficient of Mean
Deviation
◦ Co- Efficient of Variance

5. RANGE
 It is defined as the difference between
the smallest and the largest
observations in a given set of data.
 Formula is R = L – S
 Ex. Find out the range of the given
distribution: 1, 3, 5, 9, 11
 The range is 11 – 1 = 10.

6. QUARTILE DEVIATION
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) and then is divided by 2. Hence it
is half of the difference between two quartiles it
is also a semi inter quartile range.
The formula of Quartile Deviation is
(Q D) = Q3 - Q1
2

7. MEAN DEVIATION
 Mean Deviation is also known as
average deviation. In this case,
deviation taken from any average
especially Mean, Median or Mode.
While taking deviation we have to
ignore negative items and consider
all of them as positive. The formula
is given below

8. MEAN DEVIATION
The formula of MD is given below
MD = d
N (deviation taken from mean)
MD = m
N (deviation taken from
median)
MD = z
N (deviation taken from mode)

9. STANDARD DEVIATION
 It is defined as “The mean of the
squares of deviations of all the
observation from their mean.” It’s
square root is called “standard
deviation”.
 Usually it is denoted by
=
2

2

n
xx  2
)(

10. STANDARD DEVIATION
The standard deviation is represented
by the Greek letter (sigma). It is always
calculated from the arithmetic mean,
median and mode is not considered.
While looking at the earlier measures of
dispersion all of them suffer from one or
the other demerit i.e.
Range – It suffer from a serious
drawback considers only 2 values and
neglects all the other values of the

11. STANDARD DEVIATION
 Quartile deviation considers only 50% of the item
and ignores the other 50% of items in the series.
 Mean deviation no doubt an improved measure
but ignores negative signs without any basis.
 Karl Pearson after observing all these things has
given us a more scientific formula for calculating
or measuring dispersion. While calculating SD
we take deviations of individual observations
from their AM and then each squares. The sum of
the squares is divided by the number of
observations. The square root of this sum is
knows as standard deviation.

12. NO OF YOUNG
ADULTS VISIT TO
THE LIBRARY IN 10
DAYS (X)
d=X - A.M d2
40 -26 676
44 -22 484
54 -12 144
60 -6 36
62 -4 16
64 -2 4
70 4 16
80 14 196
90 24 596
96 30 900
N=10
X=660
d2= 3048

13. STANDARD DEVIATION
AM = X
N
= 660 = 66 AM
10
SD = √∑d2
N
SD =√3048 = 17.46
10
100
..
.. 
x
DS
VC