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# The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

Given:

The mean of 200 items was 50. Later on, it was discovered that the two items were misread as 92 and 8 instead of 192 and 88.

To do:

We have to find the correct mean.

Solution:

We know that,

Mean $\overline{X}=\frac{Sum\ of\ the\ observations}{Number\ of\ observations}$

Mean of 200 items $= 50$

This implies,

Total of items $= 50 \times 200$

$= 10000$

Two numbers were misread as 92 instead of 192 and 8 instead of 88.

Their difference $= 192 - 92 + 88 - 8$

$= 180$

This implies,

Correct total of items $= 10000 + 180$

$= 10180$

Correct mean $= \frac{10180}{200}$

$= 50.9$

The correct mean is 50.9.

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