Anthony wants to know the average daily high temperatures in his town during the summer. He chose two random samples of 10 consecutive days and recorded the daily high temperatures. The daily high temperatures in Fahrenheit are as follows. Sample 1: 78 82 85 87 90 85 79 86 91 88 Sample 2: 81 79 80 86 89 92 82 88 84 87 Find the mean daily high temperatures of each sample and calculate the difference between these mean daily high temperatures. Express your answer as a decimal rounded to the nearest tenth. (2 points) The mean daily high temperature of Sample 1 is ° . The mean daily high temperature of Sample 2 is ° . The mean daily high temperatures of the two samples differ by

Question

GPT-4o mini · Answer

To find the mean daily high temperatures for both samples, we will sum the temperatures of each sample and then divide by the number of days (which is 10).

Sample 1: Temperatures: 78, 82, 85, 87, 90, 85, 79, 86, 91, 88

Sum of Sample 1: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 870 \]

Mean of Sample 1: \[ \text{Mean} = \frac{\text{Sum}}{\text{Number of Days}} = \frac{870}{10} = 87.0 \]

Sample 2: Temperatures: 81, 79, 80, 86, 89, 92, 82, 88, 84, 87

Sum of Sample 2: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 870 \]

Mean of Sample 2: \[ \text{Mean} = \frac{\text{Sum}}{\text{Number of Days}} = \frac{870}{10} = 87.0 \]

Now we'll calculate the difference between the mean daily high temperatures of the two samples:

Difference: \[ \text{Difference} = |87.0 - 87.0| = 0.0 \]

Thus, the mean daily high temperature of Sample 1 is 87.0°, the mean daily high temperature of Sample 2 is 87.0°, and the mean daily high temperatures of the two samples differ by 0.0 (rounded to the nearest tenth).