Answer :
We are given the daily high temperatures for this week and last week. To find how much greater this week's median temperature is than last week's, follow these steps:
1. For this week, the temperatures are:
[tex]$$65,\,73,\,73,\,74,\,73,\,75.$$[/tex]
First, sort the temperatures:
[tex]$$65,\,73,\,73,\,73,\,74,\,75.$$[/tex]
Since there are 6 numbers (an even count), the median is the average of the third and fourth numbers. These numbers are both [tex]$73$[/tex], so the median is:
[tex]$$\frac{73 + 73}{2} = 73.$$[/tex]
2. For last week, the temperatures are:
[tex]$$68,\,51,\,62,\,66,\,85,\,72,\,72.$$[/tex]
Sorting these gives:
[tex]$$51,\,62,\,66,\,68,\,72,\,72,\,85.$$[/tex]
There are 7 numbers (an odd count), so the median is the middle number. The fourth number in the sorted list is [tex]$68$[/tex], so the median is:
[tex]$$68.$$[/tex]
3. The difference between this week’s median and last week’s median is:
[tex]$$73 - 68 = 5.$$[/tex]
Thus, this week's median temperature is [tex]$\boxed{5}$[/tex] degrees greater than last week's median temperature.
1. For this week, the temperatures are:
[tex]$$65,\,73,\,73,\,74,\,73,\,75.$$[/tex]
First, sort the temperatures:
[tex]$$65,\,73,\,73,\,73,\,74,\,75.$$[/tex]
Since there are 6 numbers (an even count), the median is the average of the third and fourth numbers. These numbers are both [tex]$73$[/tex], so the median is:
[tex]$$\frac{73 + 73}{2} = 73.$$[/tex]
2. For last week, the temperatures are:
[tex]$$68,\,51,\,62,\,66,\,85,\,72,\,72.$$[/tex]
Sorting these gives:
[tex]$$51,\,62,\,66,\,68,\,72,\,72,\,85.$$[/tex]
There are 7 numbers (an odd count), so the median is the middle number. The fourth number in the sorted list is [tex]$68$[/tex], so the median is:
[tex]$$68.$$[/tex]
3. The difference between this week’s median and last week’s median is:
[tex]$$73 - 68 = 5.$$[/tex]
Thus, this week's median temperature is [tex]$\boxed{5}$[/tex] degrees greater than last week's median temperature.
