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.

(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 first need to sum up the temperatures in each sample and then divide by the number of days (10 days in this case).

Sample 1:

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

1. Sum of Sample 1: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 87.0 + 80.0 + 178.0 + 85.0 = 847 \]

2. Mean of Sample 1: \[ \text{Mean}_1 = \frac{847}{10} = 84.7 \]

Sample 2:

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

1. Sum of Sample 2: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 79 + 86 + 89 + 82 + 87 + 84 + 88 = 875 \]

2. Mean of Sample 2: \[ \text{Mean}_2 = \frac{875}{10} = 87.5 \]

Difference Between the Means:

\[ \text{Difference} = \text{Mean}_2 - \text{Mean}_1 = 87.5 - 84.7 = 2.8 \]

Final Answers:

• The mean daily high temperature of Sample 1 is 84.7°F.
• The mean daily high temperature of Sample 2 is 87.5°F.
• The mean daily high temperatures of the two samples differ by 2.8°F.

Answer 2

Are you sure

Answer 3

Let me recalculate the mean temperatures for each sample and ensure the accuracy of the calculations.

Sample 1:

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

1. Sum of Sample 1: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 \]

   Calculating step by step:

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

   Total sum = \( 851 \)

2. Mean of Sample 1: \[ \text{Mean}_1 = \frac{851}{10} = 85.1 \]

Sample 2:

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

1. Sum of Sample 2: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 \]

   Calculating step by step:

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

   Total sum = \( 848 \)

2. Mean of Sample 2: \[ \text{Mean}_2 = \frac{848}{10} = 84.8 \]

Difference Between the Means:

\[ \text{Difference} = \text{Mean}_1 - \text{Mean}_2 = 85.1 - 84.8 = 0.3 \]

Final Answers:

• 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.

Thank you for your patience, and I appreciate your bringing this to my attention!