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.

Question

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.

Scores of Two Lacrosse Teams Lacrosse Team 1: 6 0 4 17 3 12 Lacrosse Team 2: 23 14 22 14 17 22(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 _______ °.

Answer 1

To find the mean daily high temperatures for each sample, we need to calculate the sum of the temperatures for each sample and then divide by the number of days, which is 10 for each sample.

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
= 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88
= 870

Mean of Sample 1 = Sum / Number of Days
= 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
= 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87
= 868

Mean of Sample 2 = Sum / Number of Days
= 868 / 10
= 86.8 °.

Difference Between the Means:

Difference = Mean of Sample 1 - Mean of Sample 2
= 87.0 - 86.8
= 0.2 °.

Summary of Results:

• The mean daily high temperature of Sample 1 is 87.0 °.
• The mean daily high temperature of Sample 2 is 86.8 °.
• The mean daily high temperatures of the two samples differ by 0.2 °.