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?
To find the median daily high temperature for each city, we first need to arrange the temperature data in ascending order.
For Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
The median for Dayton is 86.
For Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
The median for Laredo is 84.
Therefore, Dayton has a higher median daily high temperature, which is 86. The median for Dayton is 2 degrees higher than Laredo's median daily high temperature of 84.
Dayton is 0.5 or 0.3
To determine the exact difference between the median daily high temperatures for Dayton and Laredo, let's calculate the medians again, this time using the midpoint formula for finding the median in a set of data with an even number of values.
For Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
The midpoint values are 85 and 86. Therefore, the median for Dayton is the average of 85 and 86, which is (85+86)/2 = 85.5.
For Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
The midpoint values are 84 and 86. Therefore, the median for Laredo is the average of 84 and 86, which is (84+86)/2 = 85.
The median daily high temperature for Dayton is 85.5, and for Laredo, it is 85. The difference between these two medians is 85.5 - 85 = 0.5 degrees Fahrenheit. Therefore, Dayton's median daily high temperature is 0.5 degrees Fahrenheit higher than Laredo's median daily high temperature.