Answer :
We are given the high temperatures for two weeks. To find the difference in the medians of the temperatures, follow these steps:
1. Write down the temperatures:
This Week: [tex]$65,\,73,\,73,\,74,\,73,\,75,\,71$[/tex]
Last Week: [tex]$68,\,51,\,62,\,66,\,85,\,72,\,72$[/tex]
2. Sort each set of temperatures from least to greatest.
For This Week, the sorted list is:
[tex]$$65,\,71,\,73,\,73,\,73,\,74,\,75$$[/tex]
For Last Week, the sorted list is:
[tex]$$51,\,62,\,66,\,68,\,72,\,72,\,85$$[/tex]
3. Since there are [tex]$7$[/tex] values in each list (an odd number), the median is the middle number, which is the [tex]$4^\text{th}$[/tex] number in the sorted list.
For This Week, the median is the [tex]$4^\text{th}$[/tex] value:
[tex]$$\text{Median}_{\text{this week}} = 73$$[/tex]
For Last Week, the median is also the [tex]$4^\text{th}$[/tex] value:
[tex]$$\text{Median}_{\text{last week}} = 68$$[/tex]
4. Find how much greater this week's median is than last week's median by subtracting:
[tex]$$73 - 68 = 5$$[/tex]
Thus, this week's median high temperature is [tex]$\boxed{5}$[/tex] degrees greater than last week's.
1. Write down the temperatures:
This Week: [tex]$65,\,73,\,73,\,74,\,73,\,75,\,71$[/tex]
Last Week: [tex]$68,\,51,\,62,\,66,\,85,\,72,\,72$[/tex]
2. Sort each set of temperatures from least to greatest.
For This Week, the sorted list is:
[tex]$$65,\,71,\,73,\,73,\,73,\,74,\,75$$[/tex]
For Last Week, the sorted list is:
[tex]$$51,\,62,\,66,\,68,\,72,\,72,\,85$$[/tex]
3. Since there are [tex]$7$[/tex] values in each list (an odd number), the median is the middle number, which is the [tex]$4^\text{th}$[/tex] number in the sorted list.
For This Week, the median is the [tex]$4^\text{th}$[/tex] value:
[tex]$$\text{Median}_{\text{this week}} = 73$$[/tex]
For Last Week, the median is also the [tex]$4^\text{th}$[/tex] value:
[tex]$$\text{Median}_{\text{last week}} = 68$$[/tex]
4. Find how much greater this week's median is than last week's median by subtracting:
[tex]$$73 - 68 = 5$$[/tex]
Thus, this week's median high temperature is [tex]$\boxed{5}$[/tex] degrees greater than last week's.
