Question

The following table shows the frequency distribution of the diameters of 40 bottles. (Lengths have been measured to the nearest millimeter). Find the mean diameter.
$\begin{array}{cc}Diameter\left(mm\right)& Frequency\\ 35-39& 6\\ 40-44& 12\\ 45-49& 15\\ 50-54& 10\\ 55-60& 7\end{array}$

• A. 30
• B. 45
• C. 47
• D. 50

Answer 1

The correct option is C 47

Class mark for first class interval $=\frac{\text{Upper class limit + Lower class limit}}{2}=\frac{35+39}{2}=37$

Similarly the class mark for each class interval can be found.

$\begin{array}{cccc}Classinterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& f_i{x}_i\\ 35-39& 6& 37& 222\\ 40-44& 12& 42& 504\\ 45-49& 15& 47& 705\\ 50-54& 10& 52& 570\\ 55-60& 7& 57& 399\\ Total& \sum f_i=50& & \sum f_i{x}_i=2350\end{array}$

$Mean=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{2350}{50}=47$