To determine which temperature for city A could not have resulted in a median of [tex]\(81^\circ F\)[/tex], we need to consider the impact of each temperature option on the median of the overall temperature set.
Here are the given high temperatures for cities B, C, D, and E:
- [tex]\(87^\circ F\)[/tex] for city B
- [tex]\(81^\circ F\)[/tex] for city C
- [tex]\(62^\circ F\)[/tex] for city D
- [tex]\(93^\circ F\)[/tex] for city E
We are given four possible temperatures for city A:
a. [tex]\(85^\circ F\)[/tex]
b. [tex]\(75^\circ F\)[/tex]
c. [tex]\(65^\circ F\)[/tex]
d. [tex]\(55^\circ F\)[/tex]
Let's check each option to see if it keeps the median temperature at [tex]\(81^\circ F\)[/tex].
1. If [tex]\(t = 85^\circ F\)[/tex]:
- The temperatures would be [tex]\([62, 81, 85, 87, 93]\)[/tex].
- Sorted: [tex]\([62, 81, 85, 87, 93]\)[/tex].
- The median is [tex]\(85^\circ F\)[/tex] (since it's the middle value in the sorted list of five numbers).
- This temperature does not maintain the median at [tex]\(81^\circ F\)[/tex].
2. If [tex]\(t = 75^\circ F\)[/tex]:
- The temperatures would be [tex]\([62, 75, 81, 87, 93]\)[/tex].
- Sorted: [tex]\([62, 75, 81, 87, 93]\)[/tex].
- The median is [tex]\(81^\circ F\)[/tex] (since it's the middle value).
- This temperature maintains the median at [tex]\(81^\circ F\)[/tex].
3. If [tex]\(t = 65^\circ F\)[/tex]:
- The temperatures would be [tex]\([62, 65, 81, 87, 93]\)[/tex].
- Sorted: [tex]\([62, 65, 81, 87, 93]\)[/tex].
- The median is [tex]\(81^\circ F\)[/tex] (since it's the middle value).
- This temperature maintains the median at [tex]\(81^\circ F\)[/tex].
4. If [tex]\(t = 55^\circ F\)[/tex]:
- The temperatures would be [tex]\([55, 62, 81, 87, 93]\)[/tex].
- Sorted: [tex]\([55, 62, 81, 87, 93]\)[/tex].
- The median is [tex]\(81^\circ F\)[/tex] (since it's the middle value).
- This temperature maintains the median at [tex]\(81^\circ F\)[/tex].
From the analysis above, the temperature [tex]\(85^\circ F\)[/tex] for city A would not maintain the median of [tex]\(81^\circ F\)[/tex]. Therefore, the high temperature for city A could NOT have been:
a. [tex]\(85^\circ F\)[/tex]
