The mean of 100 observations is 20 if a number 45 is mistaken as 54 find the correct mean

19.91

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20.91

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20.09

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19.09

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Solution

The correct option is A 19.91
No .of observations $100$
Mean is $20$
Sum of observations is $20 \times 100 = 2000$
Wrong observation is $54$
$⟹ 2000 - 54 = 1946$
Correct observation is $45$
$⟹ 1946 + 45 = 1991$
Correct mean is $\frac{1991}{100} = 19.91$

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