The mean of marks scored by $100$ students was found to be $40$ Later on it was discovered that a score of $53$ was misread as $83$ . Find greatest integer value of the correct mean.

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Solution

$n = 100, x = 40$
$¯ ¯ ¯ x = \frac{1}{n} (\sum x_{i}) \Rightarrow 40 = \frac{1}{100} (\sum x_{i})$
$∴$ Incorrect value of $\sum x_{i} = 4000$
Now, Correct value of $\sum x_{i} = 4000 - 83 + 53 = 3970$
$∴$ Correct mean = $\frac{c o r r e c t v a l u e o f \sum x_{i}}{n} = \frac{3970}{100} = 39.7$
So the correct mean is $39.7$

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The mean of marks scored by 100 students was found to be 40 Later on it was discovered that a score of 53 was misread as 83. Find greatest integer value of the correct mean.

n=100,x=40¯¯¯x=1n(∑xi)⇒40=1100(∑xi)∴ Incorrect value of ∑xi=4000Now, Correct value of ∑xi=4000−83+53=3970∴ Correct mean = correctvalueof∑xin=3970100=39.7So the correct mean is 39.7

The mean of marks scored by $100$ students was found to be $40$ Later on it was discovered that a score of $53$ was misread as $83$ . Find greatest integer value of the correct mean.