Question

Answer the following questions in detail−

Calculate median from the following data-

Income in Rs	0-10	10-20	20-30	30-40	40-50	50-60
No. of persons	3	6	8	10	8	5

Answer 1

C.I.	fi	C.F
0–10	3	3
10–20	6	9
20–30	8	17
30–40	10	27
40–50	8	35
50–60	5	40
	Ʃ fi = 40

Median can be calculated using the following formula:

${\left(\frac{N}{2}\right)}^{\mathrm{th}}\mathrm{item}=\left(\frac{40}{2}\right)={20}^{\mathrm{th}}\mathrm{item}$

20^th item falls in the 27^th C.F

$\mathrm{Median}=L_1+\frac{L_2-L_1}{f_1}\times \left(\frac{N}{2}-C.F\right)$

L₁= 30
L₂= 40
fi = 10
C.F = 17

$$\begin{gathered} =30+\frac{40-30}{10}\times \left(\frac{40}{2}-17\right) \\ =30+3 \\ =33 \end{gathered}$$