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Unit 6: Dispersion: Meaning and Characteristics, Absolute and Relative Measures of Dispersion including Range...

Quartile Deviation or Semi-Interquartile Range Notes

Quartile is the location-based measure of dispersion. It measures the average amount by which the
first and the third quartiles deviate from the second quartile i.e., median.

Q– Q Q.D.
Q.D. = 3 1 , Coefficient of variation = × 100 ,
2 Median
Q– Q 1
3
Coefficient of Q.D. = .
Q + Q 1
3
Merits of Q.D.: (1) Easy to compute. (2) It is very useful to know the variability at the centre of the
data. (3) It is not much affected by the extreme items. (4) It can be calculated from open end distribution
or from a skewed distribution.
Demerits of Q.D.: (1) Based only on the middle part of the data. (2) It is not capable of further
mathematical treatment. (3) It is greatly affected by changes in sampling. (4) Gives no indication
about variation occurring beyond Q and Q .
3 1
Third Moment of Dispersion: In this method the deviations of items from mean are cubed, i.e.,
∑ d 3
Third moment of dispersion =
N

∑ d 3
N
Coefficient of third moment of dispersion =
σ
(5) It provides unit of measurement for the normal distribution.
Demerits: (1) If the data is vast, it involves tedious calculations.
Formula

Q– Q
Quartile Deviation (Q.D.) = 3 1
2
Q– Q
Coefficient of Q.D. = 3 1
Q + Q 1
3
where Q represents First Quartile
1
Q represents Third Quartile
3
Q.D. in Individual Series

Example 8: Calculate Q.D. and its coefficient from the following observations relating to marks
of 15 students:
48, 52, 56, 62, 66, 47, 51, 58, 60, 66, 68, 70, 64, 73, 63.
Solution: Array: 47, 48, 51, 52, 56, 58, 60, 62, 63, 64, 66, 66, 68, 70, 73

Q 1 = Value of the ⎡ ⎢ ⎣ N1 ⎤ 4 + ⎥ ⎦ th item

⎡ 15 1 ⎤ + th
= ⎢ ⎣ 4 ⎥ ⎦ item i.e., th item = 52
4

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