College

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

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
\multicolumn{8}{|c|}{\text{High Temperatures for This Week and Last Week}} \\
\hline
\begin{array}{c}
\text{High Temperatures} \\
\text{This Week (}\degree F\text{)}
\end{array} & 65 & 73 & 73 & 74 & 73 & 75 & 71 \\
\hline
\begin{array}{c}
\text{High Temperatures} \\
\text{Last Week (}\degree F\text{)}
\end{array} & 68 & 51 & 62 & 66 & 85 & 72 & 72 \\
\hline
\end{array}
\][/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

Answer :

First, we sort the temperatures for each week in ascending order.

For this week, the temperatures are
[tex]$$65, \;73,\; 73,\; 74,\; 73,\; 75,\; 71.$$[/tex]
When sorted, this list becomes:
[tex]$$65, \;71, \;73, \;73, \;73, \;74, \;75.$$[/tex]
Since there are 7 numbers, the median is the fourth element (when counting in order). Thus, the median for this week is
[tex]$$73.$$[/tex]

For last week, the temperatures are
[tex]$$68, \;51,\; 62,\; 66,\; 85,\; 72,\; 72.$$[/tex]
When sorted, this list becomes:
[tex]$$51, \;62, \;66, \;68, \;72, \;72, \;85.$$[/tex]
Similarly, the median is the fourth element, so the median for last week is
[tex]$$68.$$[/tex]

The difference between the medians is calculated as:
[tex]$$73 - 68 = 5.$$[/tex]

Thus, this week’s median temperature is [tex]$\boxed{5}$[/tex] degrees greater than last week’s median temperature.