Question

The mean of 30 numbers is 18. What will be the new mean, if each observation is

increased by 2.​

Answer 1

The new mean will be 20.

Explanation:

The Mean Value of a Data Set

The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:

`\displaystyle \bar x=(\sum x_i)/(n)`

Where xi is the value of each data and n is the total number of values.

The mean of n=30 numbers is
`\bar x=18`. If each observation is increased by 2, then xi'=xi+2 and the new mean value will be:

`\displaystyle \bar x'=(\sum x'_i)/(30)`

`\displaystyle \bar x'=(\sum x_i+2)/(30)`

`\displaystyle \bar x'=(\sum x_i)/(30)+(\sum 2)/(30)`

The sum of 30 times 2 is 60, thus:

`\displaystyle \bar x'=18+(60)/(30)=18+2=20`

The new mean will be 20.