High School

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

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

To determine how much greater this week's median temperature is compared to last week's, we need to find the median temperatures for each week and then compare them.

### Step-by-Step Solution:

1. List the temperatures for each week:

- This Week: 65, 73, 73, 74, 73, 75, 71
- Last Week: 68, 51, 62, 66, 85, 72, 72

2. Sort the temperatures:
- This Week (Sorted): 65, 71, 73, 73, 73, 74, 75
- Last Week (Sorted): 51, 62, 66, 68, 72, 72, 85

3. Find the median:
- The median is the middle number in a sorted list of numbers.

- This Week:
- The middle value in the sorted list of this week's temperatures (65, 71, 73, 73, 73, 74, 75) is 73.

- Last Week:
- The middle value in the sorted list of last week's temperatures (51, 62, 66, 68, 72, 72, 85) is 68.

4. Calculate the difference between the two medians:
- 73 (this week's median) - 68 (last week's median) = 5 degrees

Therefore, this week's median temperature is 5 degrees greater than last week's median temperature. The answer is 5 degrees.