x2468f4y65 x 2 4 6 8 f 4 y 6 5 If the mean of the above frequency distribution is 5.2, find y

$\begin{array}{ccccc}x& 2& 4& 6& 8\\ f& 4& y& 6& 5\end{array}$

If the mean of the above frequency distribution is 5.2, find y

Answer Details

Mean $\overline{x}$ = $\frac{\sum fx}{\sum f}$
= $\frac{5.2}{1}$
= $\frac{8+4y+36+40}{4+y+6+5}$
= $\frac{5.2}{1}$
= $\frac{84+4y}{15+y}$
= 5.2(15 + y)
= 84 + 4y
= 5.2 x 15 + 5.2y
= 84 + 4y
= 78 + 5.2y
= 84 = 4y
= 5.2y - 4y
= 84 - 78
1.2y = 6
y = $\frac{6}{1.2}$
= $\frac{60}{12}$
= 5