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 average of the temperatures recorded in each sample.

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

1. Calculate the sum of Sample 1: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 870 \]

2. Calculate the mean for Sample 1: \[ \text{Mean}_1 = \frac{\text{Sum of Sample 1}}{10} = \frac{870}{10} = 87.0 \]

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

1. Calculate the sum of Sample 2: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 868 \]

2. Calculate the mean for Sample 2: \[ \text{Mean}_2 = \frac{\text{Sum of Sample 2}}{10} = \frac{868}{10} = 86.8 \]

Difference Between the Two Means: \[ \text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 87.0 - 86.8 = 0.2 \]

So, the results 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°.