Question

Find the median for the following frequency distribution

Height (in $cm$)	$160-162$	$163-165$	$166-168$	$169-171$	$172-174$
Frequency	$15$	$117$	$136$	$110$	$14$

Answer 1

REF. Image.

Total No. of students (N) = 400

$\frac{N}{2}=200$

Median Class $=165.5-168.5$ [having nearest value $>N/2$]

Median $=l+\left[\frac{N/2-cf}{f}\right]h$

l = Lower limit of median class

cf = Cumulative frequency of class preceding median class

f = frequency of median class

h = height of class

Median $=165.5+\left[\frac{200-132}{136}\right]3$

$=165.5+\left[\frac{68}{136}\right]3=165.5+\frac{3}{2}$

$=165.5+1.5$

Median $=167cm$