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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 of each sample, we will first calculate the mean of Sample 1 and Sample 2.

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

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

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

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

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

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

Difference between the mean daily high temperatures: \[ \text{Difference} = 87.0 - 86.8 = 0.2 \]

In summary:

  • 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°.