Question

The mean of 100 observations was calculated as 40 It was found later on that one of the observations was misread as 83 instead of 53 The correct means is

• A. $40.3$
• B. $42.7$
• C. $39$
• D. $39.7$

Answer 1

The correct option is D $39.7$

$\Rightarrow$ Given mean $100$ observation $=40$

$\Rightarrow$ Sum of observations $=100\times 40=4000$

$\Rightarrow$ Given that one observation is misread as $83$ instead of $53$

$\Rightarrow$ Hence error in reading the observations $=53-83=-30$

$\Rightarrow$ Correct sum of observations $=4000–30=3970$

$\Rightarrow$ Correct mean $=\frac{3970}{100}=39.7$