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For 10 consecutive days, Anthony recorded the daily high temperatures in Dayton and Laredo. The table shows the data.

The table presents the recorded daily high temperatures (in °F) for Dayton and Laredo over a 10-day period.
Daily High Temperatures (in °
F)
Dayton 77 82 85 87 90 85 79 86 91 88
Laredo 81 79 80 86 88 92 82 88 84 87
Which city has a higher median daily high temperature? How much higher is this city’s median than the other city’s median daily high temperature?

(1 point)
Responses

Laredo has a higher median daily high temperature than Dayton by 0.5°
F.
Laredo has a higher median daily high temperature than Dayton by 0.5 degree F.

Laredo has a higher median daily high temperature than Dayton by 1°
F.
Laredo has a higher median daily high temperature than Dayton by 1 degree F.

Dayton has a higher median daily high temperature than Laredo by 0.3°
F.
Dayton has a higher median daily high temperature than Laredo by 0.3 degree F.

Dayton has a higher median daily high temperature than Laredo by 0.5°
F.

1 answer

To determine which city has a higher median daily high temperature, we need to calculate the median for both Dayton and Laredo.

First, let's organize the daily high temperatures for both cities:

Dayton Temperatures: 77, 82, 85, 87, 90, 85, 79, 86, 91, 88 Laredo Temperatures: 81, 79, 80, 86, 88, 92, 82, 88, 84, 87

Next, we will sort these temperatures in ascending order.

Sorted Dayton Temperatures:
77, 79, 82, 85, 85, 86, 87, 88, 90, 91
Median Calculation:
There are 10 temperatures, so the median will be the average of the 5th and 6th values.
5th value = 85
6th value = 86
Median for Dayton = (85 + 86) / 2 = 85.5°F

Sorted Laredo Temperatures:
79, 80, 81, 82, 84, 86, 87, 88, 88, 92
Median Calculation:
Similarly, for Laredo, the median will be the average of the 5th and 6th values.
5th value = 84
6th value = 86
Median for Laredo = (84 + 86) / 2 = 85°F

Now, comparing the two medians:

  • Median for Dayton = 85.5°F
  • Median for Laredo = 85°F

Anthony's calculated median for Dayton is higher:

Difference:
85.5 - 85 = 0.5°F

Thus, Dayton has a higher median daily high temperature than Laredo by 0.5°F.

Therefore, the correct response is: Dayton has a higher median daily high temperature than Laredo by 0.5°F.