the monthly rents (in dollars) paid by 10 people are given below. (note that these are already ordered from…

the monthly rents (in dollars) paid by 10 people are given below. (note that these are already ordered from least to greatest.) 465, 865, 915, 935, 980, 1050, 1100, 1125, 1145, 1180 send data to calculator suppose that one of the people moves. her rent changes from $465 to $665. 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 10 people are given below. (note that these are already ordered from least to greatest.) 465, 865, 915, 935, 980, 1050, 1100, 1125, 1145, 1180 send data to calculator suppose that one of the people moves. her rent changes from $465 to $665. 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 sum of original rents is $465 + 865+915+935+980+1050+1100+1125+1145+1180 = 9765$. The original mean is $\frac{9765}{10}=976.5$.

Step2: Calculate new mean

The new sum of rents is $9765 - 465+665=9965$. The new mean is $\frac{9965}{10}=996.5$. The change in mean is $996.5 - 976.5 = 20$. So the mean increases by $20$.

Step3: Analyze original median

Since $n = 10$ (even), the original median is the average of the 5th and 6th - ordered values. The 5th value is $980$ and the 6th value is $1050$, so the original median is $\frac{980 + 1050}{2}=1015$.

Step4: Analyze new median

After the change, the data - set is still of size $n = 10$ (even). The 5th and 6th ordered values remain $980$ and $1050$. So the new median is still $\frac{980 + 1050}{2}=1015$. The median stays the same.

Answer:

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