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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

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 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.

1 answer

To determine which city has a higher median daily high temperature, we first need to calculate the median for each set of temperatures.

Step 1: Sort the Data

Dayton Daily High Temperatures:
77, 82, 85, 87, 90, 85, 79, 86, 91, 88
Sorted: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91

Laredo Daily High Temperatures:
81, 79, 80, 86, 88, 92, 82, 88, 84, 87
Sorted: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92

Step 2: Calculate the Median

For a set of 10 numbers (even count), the median is the average of the 5th and 6th values.

Dayton:

  • 5th value: 85
  • 6th value: 86
    Median = (85 + 86) / 2 = 85.5°F

Laredo:

  • 5th value: 84
  • 6th value: 86
    Median = (84 + 86) / 2 = 85°F

Step 3: Compare Medians

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

Step 4: Calculate the Difference

Difference = 85.5°F - 85°F = 0.5°F

Conclusion

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

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