the monthly rents (in dollars) paid by 9 people are given below. (note that these are already ordered from…

the monthly rents (in dollars) paid by 9 people are given below. (note that these are already ordered from least to greatest.) 885, 890, 935, 955, 985, 1080, 1110, 1155, 1185 suppose that one of the people moves. his rent changes from $885 to $1065. 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 monthly rents (in dollars) paid by 9 people are given below. (note that these are already ordered from least to greatest.) 885, 890, 935, 955, 985, 1080, 1110, 1155, 1185 suppose that one of the people moves. his rent changes from $885 to $1065. 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 data set is (885, 890, 935, 955, 985, 1080, 1110, 1155, 1185). The sum of the original data (S_1=885 + 890+935 + 955+985+1080+1110+1155+1185 = 9170). The original mean (\bar{x}_1=\frac{S_1}{9}=\frac{9170}{9}\approx1018.89).

Step2: Calculate the new mean

The new data - set has one value changed from (885) to (1065). The new sum (S_2=S_1 - 885+1065=9170 - 885+1065=9350). The new mean (\bar{x}_2=\frac{S_2}{9}=\frac{9350}{9}\approx1038.89). The change in the mean is (\bar{x}_2-\bar{x}_1=\frac{9350}{9}-\frac{9170}{9}=\frac{9350 - 9170}{9}=\frac{180}{9}=20). So the mean increases by (20).

Step3: Analyze the median

The original data set has (n = 9) (an odd - numbered data set). The median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{9+1}{2}=5) - th value, which is (985). After changing (885) to (1065), the data set is still (9) values (odd - numbered). The median is still the (5) - th value, which is (985). So the median stays the same.

Answer:

(a) It increases by $20. (b) It stays the same.