Question

The mean of $8$ observations was found to be $20$. Later it was detected that one of the observations was misread as $62$. What is the correct observation, if the correct mean is $15.5$?

• A. $26$
• B. $28$
• C. $30$
• D. $29$

Answer 1

The correct option is A $26$

Mean is the sum of the data values divided by the total number of values.

Given that mean of $8$ observations is $20$

Let the values be $x_1,x_2,...,x_8$

Given that one value is $62$

Let $x_8=62$

Therefore, $\frac{x_1+x_2+...+62}{8}=20$

$⟹x_1+x_2+....+x_7+62=160$

$⟹x_1+x_2+...+x_7=98$ ————(1)

Given that $62$ is misread and the correct mean is $15.5$

Therefore, the correct mean is $15.5=\frac{x_1+x_2+...+x_8}{8}$

$⟹x_1+x_2+...+x_8=15.5\times 8=124$

$⟹98+x_8=124$

$⟹x_8=124-98=26$