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.
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.
check Approved by eNotes Editorial