Let us calculate the mean and median before and after the change in rent.
Before the change:
The mean monthly rent is given by
![\operatorname{mean}=\frac{\sum^{}_{}x_i}{n}=(845+955+985+995+1035+1055+1095)/(7)=(6965)/(7)=995]()
Mean = 995
The median monthly rent is the value in the middle of the data.
Note that the data is already sorted from least to greatest.
![\operatorname{median}=((n+1)/(2))^(th)=((7+1)/(2))^(th)=((8)/(2))^(th)=4^(th)\; value]()
The 4th value in the data set is 995
Median = 995
After the change:
Now, the rent changes from $845 to $1020
So, the data becomes
1020, 955,985, 995, 1035, 1055, 1095
Arrange the data from least to greatest.
955, 985, 995, 1020, 1035, 1055, 1095
The mean monthly rent is given by
![\operatorname{mean}=\frac{\sum^{}_{}x_i}{n}=(1020+955+985+995+1035+1055+1095)/(7)=(7140)/(7)=1020]()
Mean = 1020
The median monthly rent is the value in the middle of the data
955, 985, 995, 1020, 1035, 1055, 1095
![\operatorname{median}=((n+1)/(2))^(th)=((7+1)/(2))^(th)=((8)/(2))^(th)=4^(th)\; value]()
The 4th value in the data set is 1020
Median = 1020
(a) Change in median = 1020 - 995 = +25
It increases by $25
(b) Change in mean = 1020 - 995 = +25
It increases by $25