Question

A survey regarding the height (in cm) of $51$ girls of class X of a school was conducted and the following data was obtained:

Height in cm	Number of Girls
Less than 140	$4$
Less than 145	$11$
Less than 150	$29$
Less than 155	$40$
Less than 155	$46$
Less than 165	$51$

Find the median height.

Answer 1

Height (in cm)	f	C.F.
below 140	4	4
140-145	7	11
145-150	18	29
150-155	11	40
155-160	6	46
160-165	5	51

$N=51\Rightarrow \frac{N}{2}=\frac{51}{2}=25.5$

As 29 is just greater than 25.5, therefore median class is 145-150.

$Median=l+\frac{\frac{N}{2}+C}{f}\times h$

Here, $l=$ lower limit of median class $=145$

$C=C.F.$ of the class preceding the median class $=11$

$h=$ higher limit - lower limit $=150-145=5$

$f=$ frequency of median class $=18$

$\therefore median=145+\frac{25.5-11}{18}\times 5=145+4.03=149.03$