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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.

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.
Dayton has a higher median daily high temperature than Laredo 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.
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1 answer

To determine the median daily high temperatures for Dayton and Laredo, we first need to organize the temperatures for each city in ascending order:

Dayton temperatures:
77, 79, 82, 85, 85, 86, 87, 88, 90, 91

In sorted order:
77, 79, 82, 85, 85, 86, 87, 88, 90, 91

Laredo temperatures:
79, 80, 81, 82, 84, 86, 87, 88, 88, 92

In sorted order:
79, 80, 81, 82, 84, 86, 87, 88, 88, 92

Now, we find the median for each set of temperatures. Since both sets contain 10 numbers, the median will be the average of the 5th and 6th values.

Finding median for Dayton:

  • 5th value: 85
  • 6th value: 86
  • Median for Dayton: \( \frac{85 + 86}{2} = \frac{171}{2} = 85.5 \)

Finding median for Laredo:

  • 5th value: 84
  • 6th value: 86
  • Median for Laredo: \( \frac{84 + 86}{2} = \frac{170}{2} = 85 \)

Summary of medians:

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

Now, to find out which city has a higher median and the difference:

  • Dayton's median (85.5 °F) is higher than Laredo's median (85 °F) by \( 85.5 - 85 = 0.5 °F \).

Thus, the correct response is:

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