Question

If the observations 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 respectively and mean of these observations is 4, then find the value of 'x'.

• A. $\frac{5}{3}$
• B. $\frac{7}{4}$
• C. $\frac{2}{3}$
• D. $\frac{11}{3}$

Answer 1

The correct option is A $\frac{5}{3}$

Given:
$\begin{array}{ccccc}{x}_i& 3& 5& 7& 4\\ f_i& x& x+4& x-3& x+8\end{array}$

$\therefore \sum x_i{f}_i=3x+5(x+4)+7(x-3)+4(x+8)=3x+5x+20+7x-21+4x+32=19x+31\dots \left(i\right)$

and $\sum f_i=x+x+4+x-3+x+8=4x+9\dots \left(ii\right)$

Given, mean = 4
$\Rightarrow \frac{\sum f_i{x}_i}{\sum f_i}=4\text{From Eqs.}\left(i\right)\text{and}\left(ii\right)\frac{19x+31}{4x+9}=4$

$\Rightarrow 19x+31=16x+36\Rightarrow 3x=5\therefore x=\frac{5}{3}$