Let's start by examining the original and new datasets of monthly rents.
The original rents are: \[tex]$880, \$[/tex]910, \[tex]$975, \$[/tex]1015, \[tex]$1055, \$[/tex]1085, \[tex]$1115.
1. To find the original median, we locate the middle value of the ordered list. Since there are 7 values, the median is the 4th value:
\[
\text{Original median} = \$[/tex]1015
\]
2. To find the original mean, we sum all the rent values and divide by the number of values (7):
[tex]\[
\text{Original mean} = \frac{880 + 910 + 975 + 1015 + 1055 + 1085 + 1115}{7} = \frac{7035}{7} = \$1005
\][/tex]
Next, one person moves and their rent changes from \[tex]$880 to \$[/tex]1020. The new rents are: \[tex]$1020, \$[/tex]910, \[tex]$975, \$[/tex]1015, \[tex]$1055, \$[/tex]1085, \[tex]$1115.
1. To find the new median, we again locate the middle value of the ordered new list. Note that the new list is still ordered:
\[
\text{New median} = \$[/tex]1020.0
\]
2. To find the new mean, we sum all the new rent values and divide by the number of values (7):
[tex]\[
\text{New mean} = \frac{1020 + 910 + 975 + 1015 + 1055 + 1085 + 1115}{7} = \frac{7175}{7} = \$1025
\][/tex]
To determine the changes:
(a) Change in the median:
[tex]\[
\text{New median} - \text{Original median} = 1020 - 1015 = \$5
\][/tex]
So, the median increases by \[tex]$5.
(b) Change in the mean:
\[
\text{New mean} - \text{Original mean} = 1025 - 1005 = \$[/tex]20
\]
So, the mean increases by \[tex]$20.
\begin{tabular}{|l|l|}
\hline (a) What happens to the median? & It decreases by $[/tex]\[tex]$ \_\_\_\_\_\_. \\
It increases by $[/tex]\[tex]$ 5$[/tex]. \\
(b) What happens to the mean? & It decreases by same. [tex]$\$[/tex] \_\_\_\_\_\_. \\
& It increases by [tex]$\$[/tex] 20$. \\
& It stays the same. \\
\hline
\end{tabular}
