## Effect of Additional Data on Mean and Standard Deviation

The mean of a list of numbers is and the standard deviation is (1)

Obviously adding a numbers to the list will in general change both the mean and the standard deviation. Given the value of the mean and the standard deviation of the numbers of the original list we can find the mean and standard deviation of the new list. The procedure is:

Find then add in the extra numbers and then the new mean Rearrange the formula for the standard deviation to make the subject, obtaining so can be found.

The extra numbers in the list can be be squared then added so for the new list found.

The new standard deviation can then be found using the formula (1).

Example: The mean and standard deviation of masses of 10 members of a slimming club are 70 and 15 kg respectively. Find the mean and standard deviation when a new member of mass 90 kg joins the club. kg.

The new mean is then kg. kg2 .

With the new member kg2 .

The new standard deviation is then kg. 