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The weekly salaries (in dollars) for 9 employees of a small business are given below.(Note that these are already ordered from least to greatest.)613, 703, 773, 785, 797, 806, 815, 860, 868Suppose that the $613 salary changes to $406. Answer the following.(a)   What happens to the median? It decreases by$.It increases by$.It stays the same.(b)   What happens to the mean? It decreases by$.It increases by$.It stays the same.

Question

The weekly salaries (in dollars) for 9 employees of a small business are given below.(Note that these are already ordered from least to greatest.)613, 703, 773, 785, 797, 806, 815, 860, 868Suppose that the 613salarychangesto613 salary changes to 406. Answer the following.(a)   What happens to the median? It decreases by.Itincreasesby.It increases by.It stays the same.(b)   What happens to the mean? It decreases by.Itincreasesby.It increases by.It stays the same.

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Solution

(a) The median salary is the middle value in the ordered list. Since the list has 9 values, the median is the 5th value, which is 797.Changingthefirstvaluefrom797. Changing the first value from 613 to $406 does not affect the median, so the median stays the same.

(b) The mean salary is the sum of all the salaries divided by the number of salaries. The original sum of the salaries is 6920.Ifthe6920. If the 613 salary changes to 406,thenewsumofthesalariesis406, the new sum of the salaries is 6713. The original mean is 6920/9=6920 / 9 = 769.11 (rounded to the nearest cent). The new mean is 6713/9=6713 / 9 = 746.00 (rounded to the nearest cent). So, the mean decreases by 769.11769.11 - 746.00 = $23.11.

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