Question

Calculate the mean for the following frequency distribution using direct method.

$$\begin{array}{cccccccc}Class& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ f_i& 6& 8& 20& 25& 15& 10& 4\end{array}$$

• A. 32.4
• B. 34.2
• C. 34.6
• D. 36.4

Answer 1

The correct option is B 34.2

First we find out the class marks.

$\text{Using class marks}=\frac{\text{lower limit}+\text{upper limit}}{2}$

For the first class interval, $classmark\left(x_i\right)=\frac{0+10}{2}=5$

Similarly, class marks for other classes can be calculated.
$\begin{array}{ccccccccc}Class& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& \\ x_i& 5& 15& 25& 35& 45& 55& 65& \\ f_i& 6& 8& 20& 25& 15& 10& 4& \sum f_i=88\\ x_i{f}_i& 30& 120& 500& 875& 675& 550& 260& \sum f_i{x}_i=3010\end{array}$


$\therefore \text{Mean}=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{3010}{88}$

$=34.2$