Question

Herbert was given an assignment in which he had to find the mean of a group of nine numbers. He computed the mean as $27$. However, he later discovers that he misread $29$ as $20$, resulting in the incorrect mean calculation. What is the actual mean of the numbers given?

• A. $27$
• B. $20$
• C. $29$
• D. $28$

Answer 1

The correct option is D $28$

The mean is calculated as,

$\text{Mean}=\frac{\text{Sum of all data points}}{\text{Total number of data points}}$

The mean of $9$ numbers as computed by Herbert is $27$, thus the sum of these $9$ numbers will be,

$\begin{array}{cc}27& =\frac{\text{Sum of 9 numbers}}{9}\\ 27\times 9& =\text{Sum of 9 numbers}\\ \text{Sum of 9 numbers}& =243\end{array}$

Since, while calculating the mean, he misread $29$ as $20$, therefore the actual sum of numbers will be $29-20=9$ more.

Thus, the actual sum of given set of numbers will be,

$\begin{array}{cc}\text{Actual sum of 9 numbers}& =\text{Sum of numbers}+6\\ & =243+9\\ & =252\end{array}$

Hence, the actual mean will be

$\begin{array}{cc}\text{Actual mean}& =\frac{\text{Actual sum of 9 numbers}}{9}\\ & =\frac{252}{9}\\ & =28\end{array}$

So, option (d) is correct.