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Mr. Ellis Hintz

Feb 20, 2025

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 $60,000. 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?
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Abbie Toy

Feb 20, 2025

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: $160,000b.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: $55,000c.$60,000 = sqrt((1 / 10) (sum of squares))$3,600,000,000 = (1 / 10) (sum of squares)$36,000,000,000 = Sum of squaresOld "squares" value for the highest number: ($100,000 - $70,000)^2 = $30,000^2 = $900,000,000New "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 = $740,700,000,000Standard deviation = sqrt((1/10)($740,700,000,000)) = sqrt($74,070,000,000) = $272,158.04Answer: $272,158.04... Show More
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