Question

The weight of 10 students (in kgs) are
55, 40, 35, 52, 60, 38, 36, 45, 31, 44
The median weight is
(a) 40 kg
(b) 41 kg
(c) 42 kg
(d) 44 kg

Answer 1

(c) 42 kg

Arranging the numbers in ascending order, we have:
31, 35, 36, 38, 40, 44, 45, 52, 55, 60
Here, n is 10, which is an even number.
Thus, we have:
$$\begin{gathered} \mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{n}{2}\right)\mathrm{th}\mathrm{observation}\&\left(\frac{n}{2}+1\right)\mathrm{th}\mathrm{observation} \\ \mathrm{Median}\mathrm{weight}=\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}\left(\frac{10}{2}\right)\mathrm{th}\mathrm{student}\&\left(\frac{10}{2}+1\right)\mathrm{th}\mathrm{student} \\ =\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}5\mathrm{th}\mathrm{student}\&6\mathrm{th}\mathrm{student} \\ =\frac{1}{2}\left(40+44\right)=42 \\ \mathrm{Hence},\mathrm{the}\mathrm{median}\mathrm{weight}\mathrm{is}42\mathrm{kg}. \end{gathered}$$