Question

The table below shows 60 children in a class sorted according to their heights :

$\begin{array}{cc}\text{Height (cm)}& \text{Number of Children}\\ 140-145& 5\\ 145-150& 8\\ 150-155& 12\\ 155-160& 16\\ 160-165& 11\\ 165-170& 5\\ 170-175& 3\end{array}$

From the table , find the Median Height

• A. $156\frac{23}{32}$
• B. $156\frac{18}{32}$
• C. $155\frac{5}{16}$
• D. $156\frac{9}{16}$

Answer 1

Answer: (B), (D)

The correct options are
B

$156\frac{18}{32}$

D

$156\frac{9}{16}$

$\begin{array}{cc}\text{Height (cm)}& \text{Number of Children}\\ \text{Below}145& 5\\ \text{Below}150& 13\\ \text{Below}155& 25\\ \text{Below}160& 41\\ \text{Below}165& 52\\ \text{Below}170& 57\\ \text{Below}175& 60\end{array}$

Number of children = 60

Median = $\frac{\text{Height of 30th Child + Height of 31st child}}{2}$

Height of 30th Child = 155 + $\frac{5}{32}$ + $\frac{40}{32}$ = $156\frac{13}{32}$

Height of 31st Child = $156\frac{13}{32}$ + $\frac{5}{16}$ = $156\frac{23}{32}$

Median = $\frac{\text{Height of 30th Child + Height of 31st child}}{2}$

=$\frac{156\frac{13}{32}+156\frac{23}{32}}{2}$

= $156\frac{18}{32}$ or $156\frac{9}{16}$