Question

the mean of a set of numbers is 300. if each number in that set is increased by 5, what is the new mean of this new set of numbers?

Answer 1

The new mean of set of new numbers is 305

Solution:

Given, The mean of a set of numbers is 300

Each number in that set is increased by 5,

We have to find what is the new mean of this new set of numbers

`\text { mean }=\frac{\text { sum of observations }}{\text { number of observations }}`

Now, let the number of observations be n and observations be
`a_(1), a_(2), a_(3), a_(4), \ldots \ldots \ldots, a_(n)`

`\text { So, mean }=(a_(1)+a_(2)+a_(3)+\cdots a_(n))/(n)`

`a_(1)+a_(2)+a_(3)+\ldots \ldots+a_(n)=m e a n * n`

`a_(1)+a_(2)+a_(3)+\ldots . a_(n)=300 n`

Now, after each number is increased by 5

`\text { New numbers are }\left(a_(1)+5\right),\left(a_(2)+5\right), \ldots \ldots \ldots\left(a_(n)+5\right)`

`\text { And, new mean }=\frac{\text {sum of new observations}}{\text {number of observations}}`

`=(\left(a_(1)+5\right)+\left(a_(2)+5\right)+\ldots \ldots+\left(a_(n)+5\right))/(n)`

`=\frac{\left(a_(1)+a_(2)+\cdots a_(n)\right)+(5+5+5+\cdots+5(n\text { times)) } }{n}`

`=(300 n+5 n)/(n)=(305 n)/(n)=305`

Hence, the new mean is 305