Last week's and this week's daily high temperatures are shown in the table below.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
\multicolumn{8}{|c|}{\textbf{High Temperatures for This Week and Last Week}} \\
\hline
\begin{tabular}{c}
\textbf{High Temperatures} \\
\textbf{This Week} $\left({ }^{\circ} F \right)$
\end{tabular} & 65 & 73 & 73 & 74 & 73 & 75 & 71 \\
\hline
\begin{tabular}{c}
\textbf{High Temperatures} \\
\textbf{Last Week} $\left({ }^{\circ} F \right)$
\end{tabular} & 68 & 51 & 62 & 66 & 85 & 72 & 72 \\
\hline
\end{tabular}
\][/tex]

How much greater is this week's median temperature than last week's median temperature?

A. 2 degrees
B. 3 degrees
C. 4 degrees
D. 5 degrees

First, list the temperatures for each week:

- This week's temperatures:
[tex]$$65,\ 73,\ 73,\ 74,\ 73,\ 75,\ 71$$[/tex]

- Last week's temperatures:
[tex]$$68,\ 51,\ 62,\ 66,\ 85,\ 72,\ 72$$[/tex]

Step 1. Sort the temperatures in increasing order.

- For this week, the sorted temperatures are:
[tex]$$65,\ 71,\ 73,\ 73,\ 73,\ 74,\ 75$$[/tex]

- For last week, the sorted temperatures are:
[tex]$$51,\ 62,\ 66,\ 68,\ 72,\ 72,\ 85$$[/tex]

Step 2. Determine the median.
Since there are 7 numbers in each list, the median is the 4th number (when arranged in order).

- For this week, the 4th temperature is:
[tex]$$73$$[/tex]

- For last week, the 4th temperature is:
[tex]$$68$$[/tex]

Step 3. Compute the difference between the medians:

[tex]$$
73 - 68 = 5
$$[/tex]

Thus, this week’s median temperature is \[tex]$5^\circ F\$[/tex] greater than last week’s median temperature.