Question

The mean of 4 numbers was computed as 7, but it was later on found that 3 was misread as 8, The actual mean of this data is .

Answer 1

Given that the mean of $4$ numbers as computed is $7$. Therefore the sum of these numbers will be calculated as,

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

Since, $3$ was misread as $8$, therefore the actual sum of numbers will be $8-3=5$ less, i.e.,

$\begin{array}{cc}\text{Actual sum of numbers}& =\text{Sum of 4 numbers}-5\\ & =28-5\\ & =23\end{array}$

Hence, the actual mean is

$\begin{array}{cc}\text{Actual mean}& =\frac{23}{4}\\ & =5.75\end{array}$