# If $u_{i}=\frac{x_{i}-25}{10}, \Sigma f_{i} u_{i}=20, \Sigma f_{i}=100$, then $\bar{x}=$

Question.
If $u_{i}=\frac{x_{i}-25}{10}, \Sigma f_{i} u_{i}=20, \Sigma f_{i}=100$, then $\bar{x}=$

(a) 23

(b) 24

(c) 27

(d) 25

solution:

Given: $u_{i}=\frac{x_{i}-25}{10}, \Sigma f_{i} u_{i}=20$ and $\Sigma f_{i}=100$

Now, $u_{i}=\frac{x_{i}-A}{h}=\frac{x_{i}-25}{10}$

Therefore, $h=10$ and $A=25$

We know that

$\bar{x}=A+h\left\{\frac{1}{N} \sum f_{i} u_{i}\right\}$

$=25+10\left\{\frac{1}{100} \times 20\right\}$

$=25+10 \times \frac{1}{5}$

$=25+2$

$\bar{x}=27$

Hence, the correct option is (c).