FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 5.11

1 1 2 2

1 2

x n x n x

n n

= +

+ or,

52 40 59.75 10x^2

50

= × +

or, x 2 = 21 (on reduction) ∴required average marks = 21.

Example 13. From the following frequency table, find the value of x if mean is 23.5
Class : 50–59 40–49 30–39 20 –29 10–19 0–9
frequency : x – 4 x – 2 x + 3 x + 5 x + 10 x –2
Solution:
Table : Calculation of Arithmetic Mean
Class mid. pt. f d d ́ fd ́
(x) = x– 34.5 (d/i)
50–59 54.5 x – 4 20 2 2x – 8
40 –49 44.5 x –2 10 1 x – 2
30 – 39 34.5 x + 3 0 0 0
20 – 29 24.5 x + 5 –10 – 1 – x –5
10 – 19 14.5 x + 10 –20 – 2 – 2x – 20
0 – 9 4.5 x – 2 – 30 – 3 –3x + 6
Total N = 6x + 10 fd ́= – 3x –29

∴ Here, i = width of the class = 10.

x =

A fd ́

+ f

∑

∑ × i, or 23.5 = 34.5 +

3x 29

6x 10

− −

+ × 10 or, x = 5 (on reduction).

Example 14 : The mean salary of all employees of a company is 28,500.The mean salaries of male and female employees are 30,000 and ` 25,000 respectively. Find the percentage of males and females
employed by the company.

Let number of male employees be n 1 and that of female be n 2. We know 1 1 1 2 2 2
x n x n x
n n
= +

or,^1122
28500 30000n 25000n
n n
= +

or, 7n 2 = 3n 1 (on reduction)^12
or,n^7
n 3

Percentage of n 1 (male) = 107 ×100 70%=

,, ,, n 2 (female) = 103 ×100 30%=