Statistics Unit Test

Question

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Question
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
°
.

Answer 1

To find the mean daily high temperatures for both samples, we'll calculate the average of the temperatures in each sample.

Sample 1:
Daily High 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 = Sum / Number of Values = 870 / 10 = 87.0

Sample 2:
Daily High 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 = 868
Mean of Sample 2 = Sum / Number of Values = 868 / 10 = 86.8

Difference between Mean Daily High Temperatures:
Difference = Mean of Sample 1 - Mean of Sample 2 = 87.0 - 86.8 = 0.2

Thus, the answers are:
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 °.