Paper 4: Fundamentals of Business Mathematics & Statistic

5.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

(ii) Shortcut Method (Method of assumed Mean)

In this method, the mid-value of one class interval (preferably corresponding to the maximum frequency

lying near the middle of the distribution) is taken as the assumed mean (or the arbitrary origin) A and the

deviation from A are calculated. The mean is given by the formula :

fd

x A= +^ N where, d = x – A = (mid value) – (Assumed Mean).

Step deviation method :

x A fd i

f

= +^ ′×

, where d' =x - Ai i = scale (= width of C.I.)

Example 4: Compute the Arithmetic Mean of the following frequency distribution :

Marks No. of student

20–29 5

30 –39 11

40– 49 18

50 –59 22

60 –69 16

70–79 8

Solution:

Table: Calculation of Arithmetic Mean

Class Mid values Deviation from frequency fd

Interval x 54.5 f

d = x – 54.5

20–29 24.5 – 30 5 – 150

30–39 34.5 – 20 11 – 220

40 –49 44.5 –10 18 –180

50–59 54.5 (=A) 0 22 0

60–69 64.5 10 16 160

70 – 79 74.5 20 8 160

Total –– –– N = 80 – 550 +320

fd= – 230

∴ Arithmetic Mean

fd -230

= A +^ N = 54.5 + 80

= 54.5 – 2.875 = 51.625 = 51.6 (approx).