Question

A set of $4$ numbers was given as,


But while calculating the mean of this data, some of the students misread $1$ as $7$ and $6$ as $8$ and computed the mean.
What would be the actual mean if correct numbers were used to obtain the mean?

• A. $9$
• B. $8$
• C. $7$
• D. $8.5$

Answer 1

The correct option is C $7$

The mean as calculated by some students is,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of numbers}}{\text{Total given numbers}}\\ & =\frac{7+8+9+12}{4}\\ & =\frac{36}{4}\\ & =9\end{array}$

However, since students misread $1$ as $7$ and $6$ as $8$, therefore the actual sum of numbers will be $(7-1)+(8-6)=8$ less.

That is, the actual sum of numbers of numbers will be,

$\begin{array}{cc}\text{Actual sum of numbers}& =36-8\\ & =28\end{array}$

Therefore, the actual mean is

$\begin{array}{cc}\text{Actual Mean}& =\frac{\text{Actual sum of numbers}}{4}\\ & =\frac{28}{4}\\ & =7\end{array}$

So, option (c) is correct.