Answer :
We start by listing the average monthly high temperatures for the two cities (in °F). For City 1, the values are:
[tex]$$72,\,79,\,86,\,89,\,88,\,82,\,72,\,62,\,54,$$[/tex]
and for City 2, they are:
[tex]$$69,\,69,\,72,\,76,\,77,\,70,\,74,\,70,\,66.$$[/tex]
Notice that these values cover the months from April to December.
Next, we compare the range of high temperatures for each city. The range is calculated by subtracting the minimum temperature from the maximum temperature.
For City 1:
- The maximum temperature is [tex]$89^\circ F$[/tex].
- The minimum temperature is [tex]$54^\circ F$[/tex].
Thus, the range for City 1 is
[tex]$$89 - 54 = 35^\circ F.$$[/tex]
For City 2:
- The maximum temperature is [tex]$77^\circ F$[/tex].
- The minimum temperature is [tex]$66^\circ F$[/tex].
Thus, the range for City 2 is
[tex]$$77 - 66 = 11^\circ F.$$[/tex]
This shows that City 1 experiences a much larger variation in its high temperatures over the months compared to City 2.
To examine the summer months specifically (June, July, and August), we extract the corresponding high temperatures.
For City 1, the summer highs are:
[tex]$$86^\circ F,\,89^\circ F,\,88^\circ F.$$[/tex]
The average summer high for City 1 is calculated as
[tex]$$\frac{86+89+88}{3} \approx 87.67^\circ F.$$[/tex]
For City 2, the summer highs are:
[tex]$$72^\circ F,\,76^\circ F,\,77^\circ F.$$[/tex]
The average summer high for City 2 is
[tex]$$\frac{72+76+77}{3} = 75.0^\circ F.$$[/tex]
Thus, City 1 not only has a wider range of temperatures (due to cooler winters and hotter summers) but also experiences higher average temperatures in the summer compared to City 2.
In summary:
- City 1 shows a pronounced seasonal variation with a range of [tex]$35^\circ F$[/tex] and a higher summer average of approximately [tex]$87.67^\circ F$[/tex].
- City 2 shows more moderate fluctuations with a range of only [tex]$11^\circ F$[/tex] and a summer average of [tex]$75.0^\circ F$[/tex].
This means that City 1 experiences more extreme temperature changes throughout the year compared to City 2, which maintains more steady high temperatures year-round.
[tex]$$72,\,79,\,86,\,89,\,88,\,82,\,72,\,62,\,54,$$[/tex]
and for City 2, they are:
[tex]$$69,\,69,\,72,\,76,\,77,\,70,\,74,\,70,\,66.$$[/tex]
Notice that these values cover the months from April to December.
Next, we compare the range of high temperatures for each city. The range is calculated by subtracting the minimum temperature from the maximum temperature.
For City 1:
- The maximum temperature is [tex]$89^\circ F$[/tex].
- The minimum temperature is [tex]$54^\circ F$[/tex].
Thus, the range for City 1 is
[tex]$$89 - 54 = 35^\circ F.$$[/tex]
For City 2:
- The maximum temperature is [tex]$77^\circ F$[/tex].
- The minimum temperature is [tex]$66^\circ F$[/tex].
Thus, the range for City 2 is
[tex]$$77 - 66 = 11^\circ F.$$[/tex]
This shows that City 1 experiences a much larger variation in its high temperatures over the months compared to City 2.
To examine the summer months specifically (June, July, and August), we extract the corresponding high temperatures.
For City 1, the summer highs are:
[tex]$$86^\circ F,\,89^\circ F,\,88^\circ F.$$[/tex]
The average summer high for City 1 is calculated as
[tex]$$\frac{86+89+88}{3} \approx 87.67^\circ F.$$[/tex]
For City 2, the summer highs are:
[tex]$$72^\circ F,\,76^\circ F,\,77^\circ F.$$[/tex]
The average summer high for City 2 is
[tex]$$\frac{72+76+77}{3} = 75.0^\circ F.$$[/tex]
Thus, City 1 not only has a wider range of temperatures (due to cooler winters and hotter summers) but also experiences higher average temperatures in the summer compared to City 2.
In summary:
- City 1 shows a pronounced seasonal variation with a range of [tex]$35^\circ F$[/tex] and a higher summer average of approximately [tex]$87.67^\circ F$[/tex].
- City 2 shows more moderate fluctuations with a range of only [tex]$11^\circ F$[/tex] and a summer average of [tex]$75.0^\circ F$[/tex].
This means that City 1 experiences more extreme temperature changes throughout the year compared to City 2, which maintains more steady high temperatures year-round.
