Question

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

• A. 39.36
• B. 35.39
• C. 40.15
• D. 40.39

Answer 1

The correct option is A 39.36

Class mark for first class interval $=\frac{\text{Upper class limit + Lower class limit}}{2}=\frac{25+29}{2}=27$
Similarly the class mark for each class interval can be found.
$\begin{array}{cccc}\text{Class interval}& \text{Frequency}\left(f_i\right)& \text{Class mark}\left(x_i\right)& f_i{x}_i\\ 25-29& 4& 27& 108\\ 30-35& 14& 32& 448\\ 35-39& 22& 37& 814\\ 40-45& 16& 42& 672\\ 45-49& 6& 47& 282\\ 50-55& 5& 52& 260\\ 55-59& 3& 57& 171\\ \text{Total}& \sum f_i=70& & \sum f_i{x}_i=2755\end{array}\text{Mean}=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{2755}{70}=39.36$