Question

The mean of $100$ items is $49$. It was found that three items which should have been $60,70,80$, were wrongly read as $40,20,50$ respectively. The corrected mean is

• A. $48$
• B. $82.5$
• C. $50$
• D. $80$

Answer 1

The correct option is C $50$

Sum of $100$ items
$=n\overline{x}=49\times 100=4900$

Sum of three correct items
$=60+70+80=210$
Sum of items replaced
$=40+20+50=110$

$\therefore$ Correct sum
$=4900-110+210=5000$

Hence, the corrected mean
$=\frac{5000}{100}=50$