The mode of the following data is 67. Find the missing frequency x.

Class

40-50

50-60

60-70

70-80

80-90

Frequency

5

x

15

12

7

Solution:

Given that mode = 67

Modal class=60-70

Mode = l + (f1 – f0)h/(2f1 – f0 – f2)

Here l = lower limit of modal class=60.

h = size of class interval = 10

f1 = frequency of modal class=15

f0 = frequency of class preceding modal class=x

f1 = frequency of class succeeding modal class=12

67 = 60 + (15-x)10/(18-x)

7 = (15-x)10/(18-x)

7(18-x) = 10(15-x)

126 – 7x = 150 – 10x

3x = 24

So x = 24/3

= 8

Hence the value of x is 8.

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