Question

Last week’s and this week’s low temperatures are shown in the table below.

Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (Degrees Fahrenheit)

4

10

6

9

6
Low Temperatures
Last Week (Degrees Fahrenheit)

13

9

5

8

5

Which measures of center or variability are greater than 5 degrees? Select three choices.
the mean of this week’s temperatures
the mean of last week’s temperatures
the range of this week’s temperatures
the mean absolute deviation of this week’s temperatures
the mean absolute deviation of last week’s temperatures

Answer 1

To determine which measures of center or variability are greater than 5 degrees, let's first calculate the necessary statistical values for both weeks.

### Last Week's Temperatures
Temperatures: 13, 9, 5, 8, 5

1. **Mean** of last week:
\[
\text{Mean} = \frac{13 + 9 + 5 + 8 + 5}{5} = \frac{40}{5} = 8
\]

2. **Range** of last week:
\[
\text{Range} = 13 - 5 = 8
\]

3. **Mean Absolute Deviation** of last week:
- First, find the absolute deviations:
- |13 - 8| = 5
- |9 - 8| = 1
- |5 - 8| = 3
- |8 - 8| = 0
- |5 - 8| = 3
- Mean absolute deviation:
\[
\text{MAD} = \frac{5 + 1 + 3 + 0 + 3}{5} = \frac{12}{5} = 2.4
\]

### This Week's Temperatures
Temperatures: 4, 10, 6, 9, 6

1. **Mean** of this week:
\[
\text{Mean} = \frac{4 + 10 + 6 + 9 + 6}{5} = \frac{35}{5} = 7
\]

2. **Range** of this week:
\[
\text{Range} = 10 - 4 = 6
\]

3. **Mean Absolute Deviation** of this week:
- First, find the absolute deviations:
- |4 - 7| = 3
- |10 - 7| = 3
- |6 - 7| = 1
- |9 - 7| = 2
- |6 - 7| = 1
- Mean absolute deviation:
\[
\text{MAD} = \frac{3 + 3 + 1 + 2 + 1}{5} = \frac{10}{5} = 2
\]

### Summary of Results
- Mean of last week's temperatures: 8 (greater than 5)
- Mean of this week's temperatures: 7 (greater than 5)
- Range of last week's temperatures: 8 (greater than 5)
- Range of this week's temperatures: 6 (greater than 5)
- Mean Absolute Deviation of last week's temperatures: 2.4 (not greater than 5)
- Mean Absolute Deviation of this week's temperatures: 2 (not greater than 5)

### Final Selection
The measures of center or variability that are greater than 5 degrees are:
1. The mean of last week’s temperatures (8)
2. The mean of this week’s temperatures (7)
3. The range of this week’s temperatures (6)

Thus, the three choices are:
1. The mean of this week’s temperatures
2. The mean of last week’s temperatures
3. The range of this week’s temperatures