Question

Calculate median from the following series:

Class Interval	10−20	20−40	40−70	70−120	120−140
Frequency	4	10	26	8	2

Answer 1

Class Interval	Frequency	Cumulative Frequency
10 − 20 20 − 40	4 10	4 4 + 10 = 14 (c.f.)
(l₁) 40 − 70	26 (f)	14 + 26 = 40
70 − 120 120 − 140	8 2	40 + 8 = 48 48 + 2 = 50
	$\Sigma f$=N = 50

Median = Size of $\left(\frac{N}{2}\right)\mathrm{th}$ item
= Size of $\left(\frac{50}{2}\right)\mathrm{th}$ item
= Size of 25th item

Hence, median lies in class interval 40 − 70

$$\begin{gathered} \mathrm{Median}\mathrm{or}\mathrm{M}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{M}=40+\frac{25-14}{2}\times 30 \\ \mathrm{or},\mathrm{M}=40+\frac{11\times 30}{26} \\ \mathrm{or},\mathrm{M}=40+12.69 \\ \Rightarrow \mathrm{M}=52.69 \end{gathered}$$

Hence, the median value of the above series is 52.69