The mean mark of $100$ students was found to be $40$ . Later on, it was found that a score of $53$ was misread as $83$ . Find the correct mean corresponding to the correct score.

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Solution

Given that the total number of students $n = 100$ , $¯ ¯ ¯ x = 40$ . So,
Incorrect $\sum x = ¯ ¯ ¯ x \times n = 40 \times 100 = 4000$
Correct $\sum x =$ Incorrect $\sum x -$ wrong item $+$ correct item.
$= 4000 - 83 + 53 = 3970$
Correct $¯ ¯ ¯ x = \frac{c o r r e c t \sum x}{n}$
$= \frac{3970}{100} = 39.7$
Hence the correct mean is $39.7$ .

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The mean mark of 100 students was found to be 40. Later on, it was found that a score of 53 was misread as 83. Find the correct mean corresponding to the correct score.

Given that the total number of students n=100, ¯¯¯x=40. So,Incorrect ∑x=¯¯¯x×n=40×100=4000Correct ∑x= Incorrect ∑x− wrong item + correct item. =4000−83+53=3970Correct ¯¯¯x=correct∑xn =3970100=39.7Hence the correct mean is 39.7.

The mean mark of $100$ students was found to be $40$ . Later on, it was found that a score of $53$ was misread as $83$ . Find the correct mean corresponding to the correct score.