the weekly salaries (in dollars) for 7 employees of a small business are given below. (note that these are…

the weekly salaries (in dollars) for 7 employees of a small business are given below. (note that these are already ordered from least to greatest.) 719, 773, 788, 812, 823, 855, 1019 suppose that the $1019 salary changes to $816. 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.

the weekly salaries (in dollars) for 7 employees of a small business are given below. (note that these are already ordered from least to greatest.) 719, 773, 788, 812, 823, 855, 1019 suppose that the $1019 salary changes to $816. 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.

Answer

Explanation:

Step1: Find the original median

The data set has 7 values. The median is the 4th - value when the data is ordered. The original data set is 719, 773, 788, 812, 823, 855, 1019. The original median is 812.

Step2: Find the new median

The new data - set after changing 1019 to 816 is 719, 773, 788, 812, 816, 823, 855. The new median is still 812. So the median stays the same.

Step3: Find the original mean

The original mean $\bar{x}_1=\frac{719 + 773+788+812+823+855+1019}{7}=\frac{5889}{7}\approx841.29$.

Step4: Find the new mean

The new sum of the data set is $719 + 773+788+812+816+823+855 = 5686$. The new mean $\bar{x}_2=\frac{5686}{7}\approx812.29$. The change in the mean is $841.29−812.29 = 29$. So the mean decreases by 29.

Answer:

(a) It stays the same. (b) It decreases by $29.