Question

Give the following frequency distribution with some missing frequencies

Class

10-20

20-30

30-40

40-50

50-60

60-70

70-80

Frequency

185

f2

34

180

136

f6

50

If the total frequency is 686 and the midian is 42.6 Find out the missing frequencies f2 and f6.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} Class & Frequency & C.F. \\ \hline 10-20 & 185 & 185 \\ \hdashline 20-30 & f2 & 185+f2 \\ \hdashline 30-40 & 34 & 219+f2 \\ \hdashline 40-50 & 180& 399+f2 \\ \hdashline 50-60 & 136& 535+f2 \\ \hdashline 60-70 & f6 & 535+f2+f6 \\ \hdashline 70-80 & 50 & 585+f2+f6 \\ \hdashline \end{array}$$

The total frequency is 686

$$585+f2+f6=686$$

$$f2+f6=101$$

$median=42.6$ Then median class is $40-50.$

$l=40, h=10, f=180,$ and $C=219+f2$

$$median=l+\dfrac{N/2-C}{f}\times h$$

$$42.6=40+\dfrac{686/2-219-f2}{180}\times 10$$

$$124-f2=46.8$$

$$f2=77$$

$$f6=101-77=24$$