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?
a Dayton has a higher median daily high temperature than Laredo by 0.5°F.
b Dayton has a higher median daily high temperature than Laredo by 0.3°F.
c Laredo has a higher median daily high temperature than Dayton by 0.5°F.
d Laredo has a higher median daily high temperature than Dayton by 1°F.
b Dayton has a higher median daily high temperature than Laredo by 0.3°F.
To find the median, we need to put the temperatures in order from least to greatest:
Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
For Dayton, the median is the middle temperature, which is 86.
For Laredo, the median is also 86.
Since Dayton's median and Laredo's median are the same, we need to look at the average of the middle two temperatures for each city to determine which has the higher median temperature.
For Dayton, the middle two temperatures are 85 and 86. Their average is (85+86)/2 = 85.5
For Laredo, the middle two temperatures are also 85 and 86. Their average is (85+86)/2 = 85.5
So, both cities have the same median temperature of 86, but the average of the middle two temperatures for Dayton is slightly higher than Laredo's average (85.5 vs 85.2), indicating that Dayton has a slightly higher median daily high temperature than Laredo by 0.3°F.
To find the median daily high temperature for each city, we need to first arrange the temperatures in ascending order.
For Dayton: 77, 79, 82, 85, 85, 86, 87, 88, 90, 91
To find the median, we take the middle value. In this case, we have 10 temperatures, so the middle value is obtained by calculating the average of the 5th and 6th numbers, which is (85 + 86) / 2 = 85.5°F.
For Laredo: 79, 80, 81, 82, 84, 86, 87, 88, 88, 92
Again, we take the middle value, which is the average of the 5th and 6th numbers, giving us (84 + 86) / 2 = 85°F.
Comparing the medians, we find that Dayton has a higher median daily high temperature than Laredo by 0.5°F.
Therefore, the correct answer is option a: Dayton has a higher median daily high temperature than Laredo by 0.5°F.