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.

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

Sample 1:

Daily high temperatures: 78, 82, 85, 87, 90, 85, 79, 86, 91, 88

1. Calculate the sum: \[ 78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88 = 87.1 + 89.5 + 87 = 885 \]

2. Calculate the mean: \[ \text{Mean of Sample 1} = \frac{885}{10} = 88.5 \]

Sample 2:

Daily high temperatures: 81, 79, 80, 86, 89, 92, 82, 88, 84, 87

1. Calculate the sum: \[ 81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87 = 80 + 83.5 + 84 = 1008 \]

2. Calculate the mean: \[ \text{Mean of Sample 2} = \frac{1008}{10} = 100.8 \]

Calculate the difference between the means:

\[ \text{Difference} = 88.5 - 100.8 = -12.3 \]

The mean daily high temperature of Sample 1 is \( 88.5^\circ \).
The mean daily high temperature of Sample 2 is \( 100.8^\circ \).
The mean daily high temperatures of the two samples differ by \( 12.3^\circ \).