Question

The mean of $25$ observations is $32$. It was later discovered that $38$ and $29$ are misread as $25$ and $42$. Find the correct mean.

• A. $36$
• B. $32$
• C. $34$
• D. $33$

Answer 1

Answer: (B)

$32$

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

Given that mean of $25$ observations is $32$

Let the values be $x_1,x_2,...,x_{25}$

Given that two values are $25$ and $42$

Let $x_{24}=25$ and $x_{25}=42$

Therefore, $\frac{x_1+x_2+...+25+42}{25}=32$

$⟹x_1+x_2+....+x_{23}+67=800$

$⟹x_1+x_2+...+x_{23}=733$ ————(1)

Given that $38$ and $29$ are misread as $25$ and $42$

Therefore, the correct mean is $\frac{x_1+x_2+...+x_{23}+38+29}{25}$

$⟹\text{correct mean}=\frac{733+38+29}{25}=\frac{800}{25}=32$