Question

The median class of a frequency distribution is $125-145$. The frequency and cumulative frequency of the class preceding to the median class are $20$ and $22$, respectively. Find the sum of the frequencies, if the median is $137$.

Answer 1

Median class $=125–145$

Frequency of median class $\left(f\right)=20$

Cumulative frequency of the class preceding to the median class $\left(cf\right)=22$

Median $=137$

Class size $\left(h\right)=145–125=20$

Lower Limit of median class $\left(l\right)=125$

$\Rightarrow$ $Median=l+\frac{\frac{n}{2}-cf}{f}\times h$

$\Rightarrow$ $137=125+\frac{\frac{n}{2}-22}{20}\times 20$

$\Rightarrow$ $137-125=\frac{n-44}{2}$

$\Rightarrow$ $12=\frac{n-44}{2}$

$\Rightarrow$ $24=n-44$

$\Rightarrow$ $n=68$