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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 1° F. Laredo has a higher median daily high temperature than Dayton by 1 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. 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. Dayton has a higher median daily high temperature than Laredo by 0.3° F.

1 answer

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

Step 1: Organize the Data

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

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

Step 2: Sort the Data

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

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

Step 3: Find the Median

For a data set with an even number of entries, the median is the average of the two middle numbers.

Dayton:

  1. The middle numbers (5th and 6th in the sorted list) are 85 and 86.
  2. Median = (85 + 86) / 2 = 171 / 2 = 85.5 °F

Laredo:

  1. The middle numbers (5th and 6th in the sorted list) are 84 and 86.
  2. Median = (84 + 86) / 2 = 170 / 2 = 85 °F

Step 4: Compare Medians

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

Step 5: Calculate the Difference

Dayton's median is higher than Laredo's median by: 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.