Question

If the median of the following data is $32.5,$ find the missing frequencies.
$\begin{array}{ccccccccc}\text{Class Interval}:& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& \text{Total}\\ \text{Frequency:}& f_1& 5& 9& 12& f_2& 3& 2& 40\end{array}$

Answer 1

Class interval	Frequency	Cumulative frequency
0 – 10	f1	f1
10 – 20	5	5 + f1
20 – 30	9	14 + f1
30 – 40	12 (f)	26 + f1
40 – 50	f2	26 + f1 + f2
50 – 60	3	29 + f1 + f2
60 – 70	2	31 + f1 + f2
	N = 40

Given

Median = 32.5

The median class = 30 – 40

L = 30, h = 40 – 30 = 10, f = 12, C.F = 14 + f₁

$Median=L+\frac{\frac{N}{2}-C.F}{f}\times h$

$\Rightarrow 32.5=30+\frac{20-(14+f_1)}{12}\times 10$

$32.5-30=\frac{20-(14+f_1)}{12}\times 10$

$2.5\times 12=(6-f_1)\times 10$

$30=(6-f_1)\times 10$

$3=6-f_1$

$f_1=3$

Given

Sum of frequencies = 40

f₁ + 5 + 9 + 12 + f₂ + 3 + 2 = 40

3 + 5 + 9 + 12 + f₂ + 3 + 2 = 40

34 + f₂ = 40

f₂ = 40 – 34 = 6

f₁ = 3 and f₂ = 6