Question

40. If the mean of the following frequency distribution is 65.6, then find the missing frequencies
and
Class Interval
10-30
30-50
50-70
Total
70-90 90-110 110-130
2012
Frequency (4)
50

Answer 1

f1 = 3 and f2 = 12                

Step-by-step explanation:

Mean = 65.6

In continuous distribution, xi is the mid point of the interval.

xi in [a,b] = \frac{a+b}{2}

∑fi = 50

5+8+f1+20+f2+2 = 50

f1+f2 = 15 ..............(1)

∑xifi = 100+320+60f1 +1600+100f2+240

     = 2260+60f1+100f2 .............(2)

Mean = \frac{\sum xifi}{\sum fi}

65.6  =  \frac{2260+60f1 +100f2}{50}

60f1 + 100f2 = 1020

3f1 +5f2 = 51  ..................(2)

Solving (1) and (2) using elimination method, we get

f1 = 3 and f2 = 12