Question

The median class of a frequency distribution is 120−140. The frequency and
cumulative frequency of the class preceding to the median class are 16 and 24
respectively. Find the sum of the frequencies if the median is 135.

Answer 1

Median class =125–145

Frequency of median class (f)=20

Cumulative frequency of the class preceding to the median class (cf)=22

Median =137

Class size (h)=145–125=20

Lower Limit of median class (l)=125

⇒ Median=l+

f

2

n

−cf

×h

⇒ 137=125+

20

2

n

−22

×20

⇒ 137−125=

2

n−44

⇒ 12=

2

n−44

⇒ 24=n−44

⇒ n=68