Question

Find the value of $k$ if the mean of the following data is 17.
$$\begin{array}{cccccc}{x}_i& 10& 14& 18& 21& 25\\ f_i& 10& 15& k& 9& 9\end{array}$$

• A. 7
• B. 6
• C. 8
• D. 9

Answer 1

The correct option is A 7

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

$$\begin{array}{cccccc}{x}_i& 10& 14& 18& 21& 25\\ f_i& 10& 15& k& 9& 9\\ x_i{f}_i& 100& 210& 18k& 189& 225\end{array}$$
Mean $=\frac{\sum x_i{f}_i}{\sum f_i}$

$\sum x_i$$f_i=100+210+18k+189+225=724+k$

$\sum f_i=10+15+k+9+9=43+k$

Given that mean = 17

We can write,
$17=\frac{724+18k}{43+k}$

$\Rightarrow 724+18k$ = $17\times (43+k)$

$\Rightarrow 18k-17k=731-724$
$\Rightarrow k=7$