Ask a New Question
Menu

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

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 answer

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

Step 1: Sort the data

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

Laredo 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

The median is the average of the middle two values when the number of observations is even.

For Dayton:

  1. The sorted list is: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
  2. The middle values (5th and 6th): 85 and 86
  3. Median for Dayton = (85 + 86) / 2 = 171 / 2 = 85.5

For Laredo:

  1. The sorted list is: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
  2. The middle values (5th and 6th): 84 and 86
  3. Median for Laredo = (84 + 86) / 2 = 170 / 2 = 85

Step 3: Compare the medians

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

Step 4: Find the difference

Difference = Median of Dayton - Median of Laredo = 85.5 - 85 = 0.5

Conclusion

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