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, 88, 84, 87
Determine Dayton's median high temperature. ____ F
Determine Laredo's median high temperature. ____ F
Laredo has a _____ median temperature than Dayton by _____ F

Answer 1

To find the median high temperatures for Dayton and Laredo, we need to arrange each set of temperatures in ascending order and then find the middle value.

Dayton's High Temperatures:

Original data: 77, 82, 85, 87, 90, 85, 79, 86, 91, 88

1. Sort the temperatures: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91

2. Find the median: Since there are 10 values (an even number), the median is the average of the 5th and 6th values.

   • 5th value: 85
   • 6th value: 86

   Median for Dayton = (85 + 86) / 2 = 85.5 F

Laredo's High Temperatures:

Original data: 81, 79, 80, 86, 88, 92, 88, 84, 87

1. Sort the temperatures: 79, 80, 81, 84, 86, 87, 88, 88, 92

2. Find the median: Since there are 9 values (an odd number), the median is the middle value.

   • The middle value (5th) is 86.

   Median for Laredo = 86 F

Comparison:

Now we can compare the medians:

• Dayton's median: 85.5 F
• Laredo's median: 86 F

Laredo has a higher median temperature than Dayton by: 86 - 85.5 = 0.5 F

Final Answer:

• Dayton's median high temperature: 85.5 F
• Laredo's median high temperature: 86 F
• Laredo has a higher median temperature than Dayton by 0.5 F.