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 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.

1 answer

To find out which city has a higher median daily high temperature, we first need to sort the daily high temperatures for both Dayton and Laredo, then find the median for each city.

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

To find the median for Dayton (10 numbers, so the median will be the average of the 5th and 6th numbers): 5th number: 85 6th number: 86

Median for Dayton: \[ \text{Median}_{\text{Dayton}} = \frac{85 + 86}{2} = \frac{171}{2} = 85.5 \text{ °F} \]

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

To find the median for Laredo (10 numbers, so the median will also be the average of the 5th and 6th numbers): 5th number: 84 6th number: 86

Median for Laredo: \[ \text{Median}_{\text{Laredo}} = \frac{84 + 86}{2} = \frac{170}{2} = 85 \text{ °F} \]

Comparison of the Medians:

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

Now, we calculate the difference: \[ 85.5 - 85 = 0.5 \text{ °F} \]

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

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