There are 10 employees in a particular division of a company.?
In a particular division of a company, there are 10 employees. Their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $60,000. The highest salary in this list is $100,000. However, due to an error, this amount has been altered to $1,000,000.
a. What is the new mean salary after this change?
b. What is the new median salary after this change?
c. What is the new standard deviation after this change?
3 Answers
a.
If the mean of 10 values is $70,000, then the sum of the 10 values is $70,000 * 10, or $700,000.
Increasing the largest number from $100,000 to $1,000,000 increases the sum by $900,000, which makes it $1,600,000. Then mean then becomes $1,600,000 / 10, or $160,000.
Answer: $160,000
b.
The median is the "middle" value in the list. Increasing the largest number, or decreasing the smallest number, cannot alter the order of the list, so the middle value is still the middle value. So the median remains $55,000.
Answer: $55,000
c.
$60,000 = sqrt((1 / 10) (sum of squares))
$3,600,000,000 = (1 / 10) (sum of squares)
$36,000,000,000 = Sum of squares
Old "squares" value for the highest number: ($100,000 - $70,000)^2 = $30,000^2 = $900,000,000
New "squares" value for the highest number: ($1,000,000 - $160,000)^2 = $840,000^2 = $705,600,000,000
$36,000,000,000 - $900,000,000 + $705,600,000,000 = $740,700,000,000
Standard deviation = sqrt((1/10)($740,700,000,000)) = sqrt($74,070,000,000) = $272,158.04
Answer: $272,158.04
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