the weekly salaries (in dollars) for 8 employees of a small business are given below. (note that these are…

the weekly salaries (in dollars) for 8 employees of a small business are given below. (note that these are already ordered from least to greatest.) 708, 764, 788, 849, 883, 936, 1014, 1050 send data to calculator suppose that the $708 salary changes to $756. answer the following. (a) what happens to the mean? it decreases by $ . it increases by $ . it stays the same. (b) what happens to the median? it decreases by $ . it increases by $ . it stays the same.

the weekly salaries (in dollars) for 8 employees of a small business are given below. (note that these are already ordered from least to greatest.) 708, 764, 788, 849, 883, 936, 1014, 1050 send data to calculator suppose that the $708 salary changes to $756. answer the following. (a) what happens to the mean? it decreases by $ . it increases by $ . it stays the same. (b) what happens to the median? it decreases by $ . it increases by $ . it stays the same.

Answer

Explanation:

Step1: Calculate the original mean

The original sum of salaries is $708 + 764+788 + 849+883+936+1014+1050=6992$. The original mean is $\frac{6992}{8}=874$.

Step2: Calculate the new mean

The new sum of salaries is $(6992 - 708+756)=6992 + 48=7040$. The new mean is $\frac{7040}{8}=880$. The change in the mean is $880 - 874 = 6$, so it increases by $$6$.

Step3: Analyze the median

Since $n = 8$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The original median is $\frac{849 + 883}{2}=866$. After the change, the order of the data does not change for the middle - two values. So the median stays the same.

Answer:

(a) It increases by $6. (b) It stays the same.