Question

The weights (in $kg$) of $10$ children are:
$40,52,34,47,31,35,48,41,44,38$. Find the median weight

• A. $35.9kg$
• B. $38.4kg$
• C. $40.5kg$
• D. $42.5kg$

Answer 1

The correct option is C $40.5kg$

Arranging the weights in ascending order, we have: $31$,$34$,$35$,$38$,$40$,$41$,$44$,$47$,$48$,$52$
Here, $n=10$, which is even
$\therefore$ Median weight $=\frac{1}{2}\{{\left(\begin{array}{c}\frac{10}{2}\end{array}\right)}^{th}\text{term}+{\left(\begin{array}{c}\frac{10}{2}+1\end{array}\right)}^{th}\text{term}\}$
$=\frac{1}{2}\{5^{th}\text{term}+6^{th}\text{term}\}=\frac{1}{2}\{40+41\}kg$
$=\frac{81}{2}kg=40.5kg$
Hence, median weight $=40.5kg$