Question

The mean of 100 observation is50 if one of other observation 50 is repacef by 150 Find the resulting mean​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• We have to find the new mean

$\boxed{\sf{Mean=\frac{Sum\:of\: observation}{Number\:of\: observation}}}$

• Now given that the mean of 100 observation is 50

• let the observation be x

$\sf\implies \frac{x}{100}=50\\ \\ \sf\implies x=50\times 100\\ \\ \sf\implies x=5000$

$\boxed{\sf{observation=5000}}$

• Now if one observation is 50 replaced by 150

$\sf\implies 5000-50+150\\ \\ \sf\implies 5000+100\\ \\ \sf\implies New\: observation 5100$

$\sf\underline{\underline{\star{New\: observation=5100}}}$

• Now the mean of new observation

$\sf\implies mean\:of\:new\: observation=\cancel{\frac{5100}{100}}\\ \\ \tt\implies 51$

$\boxed{\sf{Mean\:of\:new\: observation=51}}$