Question:
If the mean of frequency distribution is $8.1$ and $\Sigma f_{i} x_{i}=132+5 k, \Sigma f_{i}=20$, then $k=$
(a) 3
(b) 4
(c) 5
(d) 6
Solution:
Given:
$\sum f_{i} x_{i}=132+5 k, \Sigma f_{i}=20$ and mean $=8.1$
Then,
Mean $=\frac{\sum f_{i} x_{i}}{\sum f_{i}}$
$8.1=\frac{132+5 k}{20}$
$162=132+5 k$
$5 k=30$
$k=6$
Hence, the correct option is (d).