Question

Find out median of the following series:

Items	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Frequency	5	10	16	18	12	10	8

Answer 1

Items	Frequency	Cumulative Frequency
20 − 30 30 − 40 40 − 50	5 10 16	5 10 + 5 = 15 15 + 16 = 31 (c.f)
50 − 60	18 (f)	31 + 18 = 49
60 − 70 70 − 80 80 − 90	12 10 8	49 + 12 = 61 61 + 10 = 71 71 + 8 = 79
	N = 79

Median or M = Size of $\left(\frac{N}{2}\right)\mathrm{th}$ item
or, M = Size of $\left(\frac{79}{2}\right)\mathrm{th}$ item
or, M = Size of 39.5th item

Hence, the median lies in the class 50-60
$$\begin{gathered} \mathrm{M}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f}{f}\times i \\ \mathrm{or},\mathrm{M}=50+\frac{39.5-31}{18}\times 10 \\ \mathrm{or},\mathrm{M}=50+\frac{8.5}{18}\times 10 \\ \mathrm{or},\mathrm{M}=50+\frac{85}{18} \\ \mathrm{or},\mathrm{M}=50+4.72 \\ \Rightarrow \mathrm{M}=54.72 \end{gathered}$$

Hence, the median is of the above series is 54.7