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

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

  1. Sum of Sample 1:
    \(78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 87 , \text{(calculated step-by-step:)} \)

    • \(78 + 82 = 160\)
    • \(160 + 85 = 245\)
    • \(245 + 87 = 332\)
    • \(332 + 90 = 422\)
    • \(422 + 85 = 507\)
    • \(507 + 79 = 586\)
    • \(586 + 86 = 672\)
    • \(672 + 91 = 763\)
    • \(763 + 88 = 851\)

    So, the sum is \(851\).

  2. Mean of Sample 1: \[ \text{Mean} = \frac{851}{10} = 85.1 \]

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

  1. Sum of Sample 2:
    \(81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 87 , \text{(calculated step-by-step:)} \)

    • \(81 + 79 = 160\)
    • \(160 + 80 = 240\)
    • \(240 + 86 = 326\)
    • \(326 + 89 = 415\)
    • \(415 + 92 = 507\)
    • \(507 + 82 = 589\)
    • \(589 + 88 = 677\)
    • \(677 + 84 = 761\)
    • \(761 + 87 = 848\)

    So, the sum is \(848\).

  2. Mean of Sample 2: \[ \text{Mean} = \frac{848}{10} = 84.8 \]

Differences in Means: To find the difference between the means of Sample 1 and Sample 2: \[ \text{Difference} = 85.1 - 84.8 = 0.3 \]

To summarize:

  • The mean daily high temperature of Sample 1 is 85.1 °F.
  • The mean daily high temperature of Sample 2 is 84.8 °F.
  • The mean daily high temperatures of the two samples differ by 0.3 °F.