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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 0.3°
F.
Dayton has a higher median daily high temperature than Laredo by 0.3 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 0.5°
F.

1 answer

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

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

First, we will sort the Dayton temperatures in ascending order: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91

Since there are 10 temperatures, the median will be the average of the 5th and 6th values:

  • 5th: 85
  • 6th: 86

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

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

Next, we will sort the Laredo temperatures in ascending order: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92

Again, since there are 10 temperatures, the median will be the average of the 5th and 6th values:

  • 5th: 84
  • 6th: 86

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

Now, we compare the two medians:

  • Median for Dayton: 85.5 °F
  • Median for Laredo: 85.0 °F

Difference:
\[ 85.5 - 85.0 = 0.5 \]

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.