the weekly salaries (in dollars) for 10 employees of a small business are given below. (note that these are…

the weekly salaries (in dollars) for 10 employees of a small business are given below. (note that these are already ordered from least to greatest.) 626, 676, 695, 724, 745, 815, 845, 847, 862, 1005 suppose that the $626 salary changes to $286. 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 10 employees of a small business are given below. (note that these are already ordered from least to greatest.) 626, 676, 695, 724, 745, 815, 845, 847, 862, 1005 suppose that the $626 salary changes to $286. 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 original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. The sum of the original salaries $S_1=626 + 676+695+724+745+815+845+847+862+1005 = 7930$. The original mean $\bar{x}_1=\frac{7930}{10}=793$.

Step2: Calculate new mean

The new sum of salaries $S_2=7930 - 626+286=7590$. The new mean $\bar{x}_2=\frac{7590}{10}=759$. The change in the mean is $793 - 759=34$, so the mean decreases by 34.

Step3: Calculate original median

Since $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. The 5th value is 745 and the 6th value is 815. The original median $M_1=\frac{745 + 815}{2}=780$.

Step4: Calculate new median

The new data - set is still ordered, and the 5th and 6th values remain 745 and 815. The new median $M_2=\frac{745 + 815}{2}=780$. So the median stays the same.

Answer:

(a) It decreases by $34. (b) It stays the same.