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.

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Solution

Step 1: Find the value of sum of terms
Given, the mean of $200$ items is $50$ .
$Mean (\bar{X}) = \frac{Sum of terms}{Number of terms}$
$\frac{x_{1} + x_{2} + x_{3} + . . . + x_{200}}{200} = 50$
$\Rightarrow x_{1} + x_{2} + x_{3} + . . . + x_{200} = 10000$
Step 2: Find the correct value of sum of terms
$Sum = x_{1} + x_{2} + x_{3} + . . . + x_{200} - 92 - 8 + 192 + 88$
$= 10000 + 180$
$= 10180$
Step 3: Find the value of correct mean
Correct mean $(\bar{X}) = \frac{10180}{200}$
$= 50.9$
Hence, the value of correct mean is $50.9$ .

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