# Arithmetic mean of 100 items of a series is 40. Later on, it was discovered that two values of 53 and 24 were wrongly taken in place of 35 and 22. Find out the correct mean.

When Arithmetic mean of 100 items is given as 40 that means sum of observations = $100\times 40=4,000$

Two values 53 & 24 were wrongly taken in place of 35 & 22; so correct mean would be as follows:

Mean = $\frac{4,000-\left(53+24\right)+\left(35+22\right)}{100}=39.80$

Regards,

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