Ask a New Question
Menu

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 __°.

1 answer

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

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

  1. Calculate the sum: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 87.0 + 85 + 79 + 86 + 91 + 88 = 870 \]

  2. Divide by the number of days (10): \[ \text{Mean for Sample 1} = \frac{870}{10} = 87.0 \]

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

  1. Calculate the sum: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 86.5 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 86.5 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 868 \]

  2. Divide by the number of days (10): \[ \text{Mean for Sample 2} = \frac{868}{10} = 86.8 \]

Now we can calculate the difference between the mean daily high temperatures of Sample 1 and Sample 2: \[ \text{Difference} = \text{Mean for Sample 1} - \text{Mean for Sample 2} = 87.0 - 86.8 = 0.2 \]

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°.