Question

Weight of eight students in kg is noted as,
71, 72, 64, 68, 70, 76, 73, 75
Find the median weight.

Answer 1

Arranging the series in the ascending order

S. No.	Weight
1 2 3 4 5 6 7 8	64 68 70 71 72 73 75 76
N = 8

$$\begin{gathered} \mathrm{Median}=\frac{\mathrm{Size}\mathrm{of}\left({\displaystyle \frac{N}{2}}\right)\mathrm{th}\mathrm{item}+\mathrm{Size}\mathrm{of}\left({\displaystyle \frac{N}{2}}+1\right)\mathrm{th}\mathrm{item}}{2} \\ \mathrm{or},\mathrm{M}=\frac{\mathrm{Size}\mathrm{of}\left({\displaystyle \frac{8}{2}}\right)\mathrm{th}\mathrm{item}+\mathrm{Size}\mathrm{of}\left({\displaystyle \frac{8}{2}}+1\right)\mathrm{th}\mathrm{item}}{2} \\ \mathrm{or},\mathrm{M}=\frac{\mathrm{Size}\mathrm{of}4\mathrm{th}\mathrm{item}+\mathrm{Size}\mathrm{of}5\mathrm{th}\mathrm{item}}{2} \\ \mathrm{or},\mathrm{M}=\frac{71+72}{2}=\frac{143}{2} \\ \Rightarrow \mathrm{M}=71.5kgs \end{gathered}$$

Hence, the median weight is 71.5 kgs.