Question

The mean of the following data is 50.
Find the value of a.

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is B 4

First we make table of given data, and finding the value of $xifi$


Mean = $\frac{\Sigma xifi}{\Sigma fi}$

here, Σ$fi$ = 13 + 15 + a + 32 +7a - 11 + 19
$⟹$Σ$fi$ = 72 +8a

and Σ$xifi$ = 130 + 450 + 30a +1600 + 490a - 770 + 1710
$⟹$Σ$xifi$ = 3120 + 520a

Value of mean given as 50,
Mean = $\frac{\Sigma xifi}{\Sigma fi}$

$⟹$ 50 = $\frac{3120+520a}{72+8a}$
50 (72 + 8a) = 3120 + 520a
3600 + 400a = 3120 + 520a
3600 - 3120 = 520a - 400a
480 = 120a
a = $\frac{480}{120}$
a = 4
Thus, the value of a is 4.