Question

The mean of $100$ items was found to be $30$. If two observation were wrongly taken as $32$ and $12$ instead of $23$ and $11$, find the correct mean.

• A. $29.4$
• B. $29.5$
• C. $29.8$
• D. $29.9$

Answer 1

Answer: (D)

$29.9$

The total no. of observations are $100$

The mean of those observations are $30$

So The sum of observations is $30\times 100=3000$

The wrong observations are $32$ and $12$

Those are to be subtracted from sum of observations

So, $3000-32-12=2956$

The correct observations are $23$ and $11$

Those are to be added

So, $2956+23+11=2990$

The mean is given by $\frac{2990}{100}=29.9$