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.

(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
°.
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Answer 1

To find the mean daily high temperatures for each sample, we will first calculate the sum of the temperatures in each sample and then divide by the number of days (10).

Sample 1:

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

Step 1: Calculate the sum of Sample 1 \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 87 + 90 + 85 + 79 + 86 + 91 + 88 + 78 + 82 + 85 = 87 + 90 + 85 + 79 + 86 + 91 + 88 + 78 + 82 + 85 = 875 \]

Step 2: Calculate the mean of Sample 1 \[ \text{Mean of Sample 1} = \frac{875}{10} = 87.5 \]

Sample 2:

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

Step 1: Calculate the sum of Sample 2 \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 872 \]

Step 2: Calculate the mean of Sample 2 \[ \text{Mean of Sample 2} = \frac{872}{10} = 87.2 \]

Calculate the difference between the means

\[ \text{Difference} = 87.5 - 87.2 = 0.3 \]

Final Results:

• The mean daily high temperature of Sample 1 is 87.5°.
• The mean daily high temperature of Sample 2 is 87.2°.
• The mean daily high temperatures of the two samples differ by 0.3°.