Answer :
To determine which measures of center or variability are greater than 5 degrees, let's analyze each measure separately.
1. Mean of This Week's Temperatures:
The temperatures for this week are: 4, 10, 6, 9, and 6.
The mean is calculated as follows:
[tex]\[ \text{Mean} = \frac{4 + 10 + 6 + 9 + 6}{5} = \frac{35}{5} = 7.0 \][/tex]
Since 7.0 is greater than 5 degrees, the mean of this week's temperatures is one of the measures.
2. Mean of Last Week's Temperatures:
The temperatures for last week are: 13, 9, 5, 8, and 5.
The mean is calculated as follows:
[tex]\[ \text{Mean} = \frac{13 + 9 + 5 + 8 + 5}{5} = \frac{40}{5} = 8.0 \][/tex]
Since 8.0 is greater than 5 degrees, the mean of last week's temperatures is another measure.
3. Range of This Week's Temperatures:
The range is calculated as the difference between the maximum and minimum temperatures.
Maximum temperature this week: 10
Minimum temperature this week: 4
[tex]\[ \text{Range} = 10 - 4 = 6 \][/tex]
Since 6 is greater than 5 degrees, the range of this week's temperatures is another measure.
4. Mean Absolute Deviation (MAD) of This Week's Temperatures:
The mean absolute deviation is calculated as the average of the absolute differences between each temperature and the mean.
The mean of this week's temperatures is 7.0.
The absolute differences are: |4 - 7|, |10 - 7|, |6 - 7|, |9 - 7|, |6 - 7| which are 3, 3, 1, 2, and 1 respectively.
[tex]\[ \text{MAD} = \frac{3 + 3 + 1 + 2 + 1}{5} = \frac{10}{5} = 2.0 \][/tex]
Since 2.0 is not greater than 5 degrees, the MAD of this week's temperatures is not one of the measures.
5. Mean Absolute Deviation (MAD) of Last Week's Temperatures:
The mean of last week's temperatures is 8.0.
The absolute differences are: |13 - 8|, |9 - 8|, |5 - 8|, |8 - 8|, |5 - 8| which are 5, 1, 3, 0, and 3 respectively.
[tex]\[ \text{MAD} = \frac{5 + 1 + 3 + 0 + 3}{5} = \frac{12}{5} = 2.4 \][/tex]
Since 2.4 is not greater than 5 degrees, the MAD of last week's temperatures is not one of the measures.
The measures of center or variability that are greater than 5 degrees are:
1. The mean of this week's temperatures (7.0 degrees)
2. The mean of last week's temperatures (8.0 degrees)
3. The range of this week's temperatures (6 degrees)
1. Mean of This Week's Temperatures:
The temperatures for this week are: 4, 10, 6, 9, and 6.
The mean is calculated as follows:
[tex]\[ \text{Mean} = \frac{4 + 10 + 6 + 9 + 6}{5} = \frac{35}{5} = 7.0 \][/tex]
Since 7.0 is greater than 5 degrees, the mean of this week's temperatures is one of the measures.
2. Mean of Last Week's Temperatures:
The temperatures for last week are: 13, 9, 5, 8, and 5.
The mean is calculated as follows:
[tex]\[ \text{Mean} = \frac{13 + 9 + 5 + 8 + 5}{5} = \frac{40}{5} = 8.0 \][/tex]
Since 8.0 is greater than 5 degrees, the mean of last week's temperatures is another measure.
3. Range of This Week's Temperatures:
The range is calculated as the difference between the maximum and minimum temperatures.
Maximum temperature this week: 10
Minimum temperature this week: 4
[tex]\[ \text{Range} = 10 - 4 = 6 \][/tex]
Since 6 is greater than 5 degrees, the range of this week's temperatures is another measure.
4. Mean Absolute Deviation (MAD) of This Week's Temperatures:
The mean absolute deviation is calculated as the average of the absolute differences between each temperature and the mean.
The mean of this week's temperatures is 7.0.
The absolute differences are: |4 - 7|, |10 - 7|, |6 - 7|, |9 - 7|, |6 - 7| which are 3, 3, 1, 2, and 1 respectively.
[tex]\[ \text{MAD} = \frac{3 + 3 + 1 + 2 + 1}{5} = \frac{10}{5} = 2.0 \][/tex]
Since 2.0 is not greater than 5 degrees, the MAD of this week's temperatures is not one of the measures.
5. Mean Absolute Deviation (MAD) of Last Week's Temperatures:
The mean of last week's temperatures is 8.0.
The absolute differences are: |13 - 8|, |9 - 8|, |5 - 8|, |8 - 8|, |5 - 8| which are 5, 1, 3, 0, and 3 respectively.
[tex]\[ \text{MAD} = \frac{5 + 1 + 3 + 0 + 3}{5} = \frac{12}{5} = 2.4 \][/tex]
Since 2.4 is not greater than 5 degrees, the MAD of last week's temperatures is not one of the measures.
The measures of center or variability that are greater than 5 degrees are:
1. The mean of this week's temperatures (7.0 degrees)
2. The mean of last week's temperatures (8.0 degrees)
3. The range of this week's temperatures (6 degrees)
