Question

The mean of the following distribution is:
$$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\end{array}$$

• A. 15.2
• B. 15.35
• C. 15.55
• D. 16

Answer 1

The correct option is C

15.55

Average or mean value of a given number of observations is the sum of all the observations divided by the total number of observations.

$$\begin{array}{ccccc}{x}_i& 10& 13& 16& 19\\ f_i& 2& 5& 7& 6\\ x_i{f}_i& 20& 65& 112& 114\end{array}$$
$\text{mean}=\frac{\sum x_i{f}_i}{\sum f_i}$

$\sum x_i$$f_i=20+65+112+114=311$

$\sum f_i=20$

Hence, $\text{mean}=\frac{\sum x_i{f}_i}{\sum f_i}=\frac{311}{20}=15.55$