Question

if the mean of the following data is $7.5$, then find the value of 'A'.

Marks	$5$	$6$	$7$	$8$	$9$	$10$
No. of students	$3$	$10$	$17$	$A$	$8$	$4$

Answer 1

Marks (x1) No of students (f1) x1f1

5 3 15

6 10 60

7 17 119

8 A 8A

9 8 72

10 4 0

Total 42+A 306+8A

Sum of frequency (f1) =$42+A$

Sum of f1x1 = $306+8A$

Given mean is $7.5$

Mean $\overline{x}=\frac{\Sigma f_1{x}_1}{\Sigma f_1}$

$\therefore 7.5=\frac{306+8A}{41+A}$

$\Rightarrow 306+8A=7.5(42+A)$

$\Rightarrow 306+8A=315+7.5A$

$\Rightarrow 8A-7.5A=315-306$

$\Rightarrow 0.5A=9$

$\Rightarrow A=18$