Paper 4: Fundamentals of Business Mathematics & Statistic

5.44 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

or, Q 3 – 30 =7. 105 ×^10 = 7.5

or, Q 3 = 30+ 7.5 = 37.5

Quartile Deviation = Q^32 −Q^1 =37.5 21.4 2 − =8.05

Example 42 : Calculate the appropriate measure of dispersion from the following data :

Wages in rupees per week No. of wages earners

less than 35 14

35-37 62

38-40 99

41-43 18

over 43 7

Solution: Since there are open-end classes in the frequency distribution. Quartile deviation would be the

most appropriate measure of dispersion for the data. So, we have to determine the quartiles QI and Q 3

which can be done from cumulative frequency distribution using simple interpolation.

Table : Cumulative Frequency Distribution

Wages (`) per week Cumulative frequency

34.5 14

QI→ ←N/4=50

37.5 76

Q 3 → ← 3N/4= 150

40.5 175

43.5 193

...... 200 = N

Applying Simple interpolation,

Q 34.5 1

37.5 34.5

−

− =

50 14

76 14

−

− and

Q 3 37.5

40.5 37.5

−

− =

150 76

175 76

−

−

Solving QI = ` 36.24 Q 3 = ` 39.74

Therefore, Quartile Deviation =(39.74 36.24) 2 − =1.75

5.3 MEASURES OF DISPERSION

5.3.1. DISPERSION

A measure of dispersion is designed to state the extent to which individual observations (or items) vary from

their average. Here we shall account only to the amount of variation (or its degree) and not the direction.

Usually, when the deviation of the observations form their average (mean, median or mode) are found out

then the average of these deviations is taken to represent a dispersion of a series. This is why measure of

dispersion are known as Average of second order. We have seen earlier that mean, median and mode,

etc. are all averages of the first order.