Question

The mean of $20$ observations was found to be $40$. It was later discovered that $25$ and $36$ were misread as $23$ and $42$, then find the correct mean.

• A. $41$
• B. $39$
• C. $38.8$
• D. $39.8$

Answer 1

Answer: (D)

$39.8$

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

Given that mean of $20$ observations is $40$

Let the values be $x_1,x_2,...,x_{20}$

Given that two values are $23$ and $42$

Let $x_{19}=23$ and $x_{20}=42$

Therefore, $\frac{x_1+x_2+...+23+42}{20}=40$

$⟹x_1+x_2+....+x_{18}+65=800$

$⟹x_1+x_2+...+x_{18}=735$ ————(1)

Given that $25$ and $36$ are misread as $23$ and $42$

Therefore, the correct mean is $\frac{x_1+x_2+...+x_{18}+25+36}{20}$

$⟹\text{correct mean}=\frac{735+25+36}{20}=\frac{796}{20}=39.8$