Question

The following table shows the frequency distribution of the ages of 35 people. Find the mean of the data.
$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency\left(f\right)& 5& 15& 10& 2& 3\end{array}$

• A. 16.5
• B. 32.7
• C. 20.1
• D. 45.8

Answer 1

The correct option is C 20.1

Here, class mark of the first interval =$\frac{Lowerclasslimit+Upperclasslimit}{2}$
$=\frac{0+10}{2}=5$

Similarly, we can find the midpoints of all the class intervals.
$\begin{array}{cccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}\left(f_i\right)& 5& 15& 10& 2& 3\\ \text{class mark}\left(x_i\right)& 5& 15& 25& 35& 45\\ f_i{x}_i& 25& 225& 250& 70& 135\end{array}$

$\sum f_i$ = 5 + 15 + 10 + 2 + 3
= 35

$\sum f_i{x}_i$ = 25 + 225 + 250 + 70 + 135
= 705

$Mean=\frac{\sum f_i{x}_i}{\sum f_i}$
$=\frac{705}{35}$
$=20.1$