Question

In the following data, find the values of $p$ and $q$ Also, find the median class and modal class.

$\begin{array}{ccc}\text{Class}& \text{Frequency(f)}& \text{Cumulative~frequency(cf)}\\ 100-200& 11& 11\\ 200-300& 12& p\\ 300-400& 10& 13\\ 400-500& q& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\end{array}$

Answer 1

$\begin{array}{ccc}\text{Class}& \text{Frequency(f)}& \text{Cumulative~frequency(cf)}\\ 100-200& 11& 11\\ 200-300& 12& p\\ 300-400& 10& 13\\ 400-500& q& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\end{array}$

From the table,

$P=11+12=23$

$11+12+10+q=46$

$33+q=46$

$q=46-33=13$

i.e., the frequency table is

$\begin{array}{ccc}\text{Class}& \text{Frequency(f)}& \text{Cumulative~frequency(cf)}\\ 100-200& 11& 11\\ 200-300& 12& 23\\ 300-400& 10& 13\\ 400-500& 13& 46\\ 500-600& 20& 66\\ 600-700& 14& 80\end{array}$

In the table, highest frequency is $20$.

$\Rightarrow$ Modal class is $500-600$---(1)

Sum of the frequencies $N=80$

$\frac{N}{2}=40$ the observation lies in the Class $400-500$

Hence, Median class is $400-500$---(2)