A set of numbers has a mean of 36 and a standard deviation of 8. A constant is added to increase the mean to 40, how is standard deviation altered.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The mean of a set of numbers is given by `barx = (sum_(i = 1)^n x_i)/n` and the standard deviation is given by `sqrt((sum_(i = 1)^n (x_i - barx))/(n - 1))`

If a constant term is added to all the terms to increase the mean, the new standard deviation is...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

The mean of a set of numbers is given by `barx = (sum_(i = 1)^n x_i)/n` and the standard deviation is given by `sqrt((sum_(i = 1)^n (x_i - barx))/(n - 1))`

If a constant term is added to all the terms to increase the mean, the new standard deviation is `sqrt((sum_(i = 1)^n (x_i + C - (barx + C)))/(n - 1))`

=> `sqrt((sum_(i = 1)^n (x_i - barx))/(n - 1))`

This shows that the standard deviation is not changed.

If a constant is added to each of a set of numbers to increase the mean from 36 to 40 there is no change in the standard deviation and it remains 8.

Approved by eNotes Editorial Team