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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.
Updated on: 10-Oct-2022
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