There are 10 employees in a particular division of a company. Their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000. The largest number on the list is $100,000. By accident, this number is changed to $1,000,000.
a. What is the value of the mean after the change?
b. What is the value of the median after the change?
c. What is the value of the standard deviation after the change?
(a) We will work in units of $1000. Let 
be the sum of the original 10 numbers and let 
be the sum after the change. Then 
?10 = 70, so = 700. Now 
= – 100 + 1000 = 1600, so the new mean is ?10 = 160.
(b) The median is unchanged at 55.
(c) Let 
be the original 10 numbers. Let 
. Then the variance is 
= 400, so 
= 52,600. Let 
be the sum of the squares after the change. Then 
= 1,042,600. The new standard deviation is 
= 295.63 .
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