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 [ ? ]°.

Answer 1

To find the mean daily high temperatures for each sample, we will calculate the average of the daily high temperatures listed.

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

1. Calculate the sum of Sample 1: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 88 + 87 + 90 + 85 + 79 + 86 + 91 + 88 + 82 + 78 = 878 \]

2. Count the number of days (n = 10): \[ \text{Mean of Sample 1} = \frac{\text{Sum of Sample 1}}{n} = \frac{878}{10} = 87.8 \]

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

1. Calculate the sum of Sample 2: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 86 + 89 + 92 + 82 + 88 + 84 + 87 + 81 + 79 + 80 = 88 + 86 + 89 + 82 + 81 + 79 + 80 + 92 + 84 + 87 = 876 \]

2. Count the number of days (n = 10): \[ \text{Mean of Sample 2} = \frac{\text{Sum of Sample 2}}{n} = \frac{876}{10} = 87.6 \]

Now, calculate the difference between the mean daily high temperatures of the two samples: \[ \text{Difference} = \text{Mean of Sample 1} - \text{Mean of Sample 2} = 87.8 - 87.6 = 0.2 \]

Answers:

• The mean daily high temperature of Sample 1 is 87.8°.
• The mean daily high temperature of Sample 2 is 87.6°.
• The mean daily high temperatures of the two samples differ by 0.2°.