Question

If the numbers 3, 5, 7, 4 have frequencies x, x+4, x-3, x+8 with their arithmetic mean of 4, then x will be _____.

• 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 $\frac{\sum f_i{x}_i}{\sum f_i}=4\Rightarrow \frac{19x+31}{4x+9}=4$
[From Eqs.(i) and (ii)]
$\Rightarrow 19x+31=16x+36\Rightarrow 3x=5\therefore x=\frac{5}{3}$