Question

Find the missing frequencies in the following frequency distribution if the mean is 50.25 and the total number of students in class is 80 marks obtained 25,35,45,55,65,75,85.No of students 7,23,x,15,10,y,5.

Answer 1

Solution:

Mean =50.25

$mean \: = \frac{\Sigma x_{i}f_{i}}{\Sigma f_{i}} \\ \\ 50.25 = \frac{25 \times 7 + 35 \times 23 + 45x + 55 \times 15 + 65 \times 10 + 75y + 85 \times 5}{7 + 23 + x + 15 + 10 + y + 5} \\ \\ 50.25= \frac{175 + 805 + 45x + 825 + 650 + 75y + 425}{80} \\ \\ 1340= 960 + 15x + 25y \\ \\ 960 + 15x + 25y=1340 \\ \\15x+25y=380 \\\\3x+5y = 76...eq1$
Second equation is

$60 + x + y = 80 \\ \\ x + y = 20...eq2$

on solving eq1 and 2 you get th values of missing Frequencies x and y.

Multiply eq2 by 3 and subtract both eq1 and 2

3x+3y=60
3x+5y=76
________
-2y=-16

y= 8

and x+8= 20

x= 20-8

x= 12

Thus missing Frequencies are x = 12 and y = 8

Hope it helps you.