Question

Determine the missing frequency x from the following data when the mode is 67
40-50; 50-60; 60-70; 70-80; 80-90
5 x 15 12 7

Answer 1

class f

40-50 5

50-60 x

60-70 15

70-80 12

80-90 7

mode = L + (f1-f0/2f1-f0-f2)h

67 = 60+(15-x /30-x-12)10

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

7/10=15-x/18-x

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

126-7x=150-10x

3x=24

x=8

Answer 2

Answer: x= 8

Step-by-step explanation:

C.I                        f

40-50                 5

50-60                 x

60-70                 15

70-80                  12

80-90                   7

As form given the mode is 67 which lies in 60-70

therefore L= 60

$f_1=15 , f_0= x ,f_2= 12$

Now as we know

$Mode=L+ \dfrac{f_1-f_0}{2f_1-f_0-f_2} \times h \\\\\Rightarrow 67 = 60+ \dfrac{15-x}{2\times 15-x- 12} \times 10\\\\\Rightarrow 7= \dfrac{15-x}{18-x} \times 10\\\\\Rightarrow 126- 7x= 150-10x\\\\\Rightarrow 3x= 24\\\\\Rightarrow x= 8$

Hence, the missing frequency is 8