Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.43

Quartile Deviation (Q.D.) is dependent on the two quartiles and does not take into account the variability
of the largest 25% or the smallest 25% of observations. It is therefore unaffected by extreme values. Since in
most cases the central 50% of observation tend to be fairly typical, Q.D. affords a convenient measure of
dispersion. It can be calculated from frequency distributions with open-end classes. Q.D. is thus superior to
Range in many ways. Its unpopularity lies in the fact that Q.D. does not depend on the magnitudes of all
observations. The calculation of Q.D. only depends on that of the two quartiles, Q1 and Q3 which can be
found from a cumulative frequency distribution using simple interpolation.
Example 41 : Calculate the quartile deviation from the following:

Class interval 10-15 15-20 20-25 25-30 30-40 40-50 50-60 60-70 Total

Frequency 4 12 16 22 10 8 6 4 82

Solution :
In order to compute Quartile Deviation, we have to find QI and Q 3 i.e. values of the
variable corresponding to Cumulative frequencies N/4 and 3N/4. Here, total frequency N= 82.
Therefore, N/4 = 20.5 and 3N/4 = 61.5

Cumulative Frequency Distribution

Class Boundary Cumulative Frequency (less - than)

10 0

15 4

20 16

Q 1 → ←N/4 = 20.5

25 32

30 54

Q 3 → ←3N/4 = 61 .5

40 64

50 72

60 78

70 82 = N

Applying simple interpolation,
Q 1 20 20.5 16
25 20 32 16

− = −

− −

or, Q 20^15 − = 4.5 16

or, Q 1 – 20 = 4.5 16 ×^5 = 1.4

or, Q 1 = 20+ 1.4 = 21.4
Similarly
Q 3 30
40 30

−

− =

61.5 30

64 54

−

−

or, Q^310 −^30 = 7.5 10