Question

While calculating the mean of $3$ single-digit numbers, Xavier mistakenly replaced the number $6$ by $9$, and obtained the mean as $5$. Find the actual mean of the data set.

• A. 4

Answer 1

The correct option is A 4
While calculating the mean of $3$ single-digit numbers, Xavier replaced $6$ by $9$, and obtained the mean as $5$.
Consider, the other $2$ single-digit numbers are $\left[\right]\text{and}\left[\right]$.

As Xavier obtained the mean of data set $\left\{\right[],[],9\}$ as $5$, we can write

$\frac{\left[\right]+\left[\right]+9}{3}=5$

$\Rightarrow \frac{\left[\right]+\left[\right]+9}{3}\times 3=5\times 3$
(multiplying $3$ in both sides)

$\Rightarrow \left[\right]+\left[\right]+9=15$

$\Rightarrow \left[\right]+\left[\right]+9-9=15-9$
(substracting $9$ from both sides)

$\Rightarrow \left[\right]+\left[\right]=6$

$\text{Need to find:}$ Actual mean of the data set $\left\{\right[],[],6\}$, i.e.,

$\frac{\left[\right]+\left[\right]+6}{3}$

$=\frac{6+6}{3}$
$(\because []+[]=6)$

$=\frac{12}{3}=4$

$\therefore$ The actual mean of the data set is $4$.