Question

Find the mean age in years from the frequency distribution given below.
$\begin{array}{cc}Classintervalofageinyears& Frequency\left(f_i\right)\\ 25-29& 4\\ 30-34& 14\\ 35-39& 22\\ 40-44& 16\\ 45-49& 6\\ 50-54& 5\\ 55-59& 3\\ Total& 70\end{array}$

• A. 39.35
• B. 39.39
• C. 40.15
• D. 40.39

Answer 1

The correct option is A 39.35

First we convert the class interval into continuous class interval. We subtract 0.5 from the lower limit and add 0.5 to the upper limit of the each class interval.

Class mark for first class interval $=\frac{\text{Upper class limit + Lower class limit}}{2}=\frac{24.5+29.5}{2}=27$
Similarly the class mark for each class interval can be found.
$\begin{array}{cccc}Classinterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& f_i{x}_i\\ 24.5-29.5& 4& 27& 108\\ 29.5-34.5& 14& 32& 448\\ 34.5-39.5& 22& 37& 814\\ 39.5-44.5& 16& 42& 672\\ 44.5-49.5& 6& 47& 282\\ 49.5-54.5& 5& 52& 260\\ 54.5-59.5& 3& 57& 171\\ Total& \sum f_i=70& & \sum f_i{x}_i=2755\end{array}Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{2755}{70}=39.4$