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

Question

  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 0.3°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.

Answer 1

To find the median daily high temperature for both Dayton and Laredo, we first need to organize their temperatures in ascending order and then calculate the median.

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

Organizing Dayton's temperatures in ascending order: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91

Since there are 10 data points, 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

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

Organizing Laredo's temperatures in ascending order: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92

Again, since there are 10 data points, 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

Comparing the Medians:

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

Dayton's median is higher than Laredo's median by: 85.5°F - 85°F = 0.5°F

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