Question

Allen was given a set of $7$ numbers and was asked to calculate the mean. She computed the value of mean as $14$. But later teacher informed her that she computed the wrong mean by taking $8$ in place of $6$ and asked her to obtain the correct mean. So, what will be the actual mean?

• A. $14$
• B. $13.71$
• C. $16$
• D. $12$

Answer 1

The correct option is B $13.71$

The formula to calculate the mean is,

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

Given the mean of $7$ numbers as computed by Allen is $14$. Therefore, the sum of these $7$ numbers will be,

$\begin{array}{cc}14& =\frac{\text{Sum of 7 numbers}}{7}\\ 14\times 7& =\text{Sum of 7 numbers}\\ \text{Sum of 7 numbers}& =98\end{array}$

Since, she calculated the mean by taking $8$ instead of $6$, therefore the actual sum of $7$ numbers will be $8-6=2$ less.

Thus, the actual sum of $7$ numbers is,

$\begin{array}{cc}\text{Actual sum of 7 numbers}& =\text{Sum of 7 numbers}-2\\ & =98-2\\ & =96\end{array}$

Therefore, the actual mean will be calculated as,

$\begin{array}{cc}\text{Actual mean}& =\frac{\text{Actual sum of 7 numbers}}{7}\\ & =\frac{96}{7}\\ & =13.71\end{array}$

So, option (b) is correct.