Two psychology professors assesses students’ assignment with average 38 marks (out of 50). Does this indicate that both teachers have same evaluation temperament (assuming such may be disastrous!). Let us consider (i) teacher A awards within 34 to 40 marks, (ii) while teacher B awards within 20 to 48 marks. If you are a student and seeking to get your assignment assessed which teacher you will prefer??

1. Variability: An Introduction
Dr Rajesh Verma
Asst. Prof (Psychology)
Govt. College Adampur, Hisar, Haryana

2. Case
Two psychology professors assesses students’
assignment with average 38 marks (out of 50). Does this
indicate that both teachers have same evaluation
temperament (assuming such may be disastrous!). Let us
consider
(i) teacher A awards within 34 to 40 marks,
(ii) while teacher B awards within 20 to 48 marks.
If you are a student and seeking
to get your assignment assessed which
teacher you will prefer??
If you are puzzled do not worry,
study of ‘variability’ will help you.

3. Meaning
Variability means the ability to vary. It has come
from word ‘variable’ which means
‘not staying the same’ or ‘often
changing’. A situation, quantity, or
number which is not constant or that
can vary.
For example, ‘memory’ and
‘intelligence’ are variables.

4. Definition
An index of scattering of scores around the mean
(center of distribution) is called variability. It is also
known as Spread, Dispersion or Width (Levin & Fox,
2006).
Variability measures how much the scores vary
from each other.

5. Introduction
Nature has complexity as well as simplicity in
its creations and follows a pattern. The complexity in
the nature inherently occurs due to inter and intra-
creations ‘variability’. For example; two rose flowers
grown on the same plant are similar yet different.
Two chapattis prepared by same cook under similar
conditions are similar yet different. Even different
coloured flowers grow
on same plant.

6. Understanding with Figures
Now it’s time for you to tell, out of
A & B which figure have higher
variability/
spread/
dispersion in
terms of size of
the circles.

7. Understanding with Graph
In this figure the data represented
by B has higher
dispersion than
data represented
by A. It shows
B has higher
variability in its
data set
than A.

8. Measures of Variability
1. Range,
2. Interquartile range,
3. Mean deviation,
4. Variance, and
5. Standard
deviation.

9. 1. Range – The difference between
the highest and lowest score in a data
set.
For example – In the given data set
lowest score is 4 and highest score is
30 therefore, 30-4 = 26, So, range is
26. So simple isn’t it?
Data Set
4
21
14
8
25
30
11
20
19
26
10

10. 2. Interquartile Range – Range of middle 50% values
of a data set. Or distance between the first and third
quartile i.e. IQR = Q3-Q1
3. Mean Deviation – Average of absolute differences
of raw score from there mean.
MD =
∑|𝒙− 𝒙|
𝑵
Where, ∑ = Summation
x = score
𝒙 = mean
N = no. of score
| = Absolute

11. 4. Variance (s) – It is the average of the squared
differences of each raw score from the mean.
It is denoted by ‘s’. 𝒔 𝟐
=
∑(𝒙− 𝒙) 𝟐
𝑵
5. Standard Deviation (σ) – The square root of
variance. It represents the average variability in a data
set because it measures the average of deviations from
the mean. σ =
∑(𝒙− 𝒙) 𝟐
𝑵
Where, ∑ = Summation
x = score
𝒙 = mean
N = no. of score
s = variance

12. References:
1. Levin, J & Fox, J. A. (2006). Elementary statistics
in in social research. Delhi: Dorling Kindersley (India).
2. http://sphweb.bumc.bu.edu
/otlt/mph-modules/bs/bs704_
summarizingdata/bs704_
summarizingdata7.html.

13. vermasujit@yahoo.com
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Quartile Deviation