The mean of $20$ numbers is $59$ . If $3$ is added to each number what will be the new mean?

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Solution

Let $x_{1}, x_{2}, . . . ., x_{20}$ be the $20$ numbers
Mean $= \frac{x_{1} + x_{2} + . . . . + x_{20}}{20} = 59$
$∴ x_{1} + x_{2} + . . . . + x_{20} = 1180$
New Mean $= \frac{(x_{1} + 3) + (x_{2} + 3) + . . . . + (x_{20} + 3)}{20}$
$= \frac{1180 + 60}{20} = 62$

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