To determine which measures of center or variability are greater than 5 degrees, we'll need to evaluate the following statistics for both this week and last week:
1. Mean of this week's temperatures
2. Mean of last week's temperatures
3. Range of this week's temperatures
4. Mean absolute deviation (MAD) of this week's temperatures
5. Mean absolute deviation (MAD) of last week's temperatures
### Mean of this week's temperatures
This week's temperatures: \(4, 10, 6, 9, 6\)
Mean: \(\frac{4 + 10 + 6 + 9 + 6}{5} = \frac{35}{5} = 7.0\)
### Mean of last week's temperatures
Last week's temperatures: \(13, 9, 5, 8, 5\)
Mean: \(\frac{13 + 9 + 5 + 8 + 5}{5} = \frac{40}{5} = 8.0\)
### Range of this week's temperatures
This week's temperatures: \(4, 10, 6, 9, 6\)
Range: \(10 - 4 = 6\)
### Mean absolute deviation of this week's temperatures (MAD)
This week's temperatures: \(4, 10, 6, 9, 6\)
Mean: \(7.0\)
Deviations from the mean: \(|4 - 7|, |10 - 7|, |6 - 7|, |9 - 7|, |6 - 7| = 3, 3, 1, 2, 1\)
MAD: \(\frac{3 + 3 + 1 + 2 + 1}{5} = \frac{10}{5} = 2.0\)
### Mean absolute deviation of last week's temperatures (MAD)
Last week's temperatures: \(13, 9, 5, 8, 5\)
Mean: \(8.0\)
Deviations from the mean: \(|13 - 8|, |9 - 8|, |5 - 8|, |8 - 8|, |5 - 8| = 5, 1, 3, 0, 3\)
MAD: \(\frac{5 + 1 + 3 + 0 + 3}{5} = \frac{12}{5} = 2.4\)
### Summary of Measures Greater Than 5 Degrees
- Mean of this week's temperatures: \(7.0\) (greater than \(5\))
- Mean of last week's temperatures: \(8.0\) (greater than \(5\))
- Range of this week's temperatures: \(6\) (greater than \(5\))
- MAD of this week's temperatures: \(2.0\) (not greater than \(5\))
- MAD of last week's temperatures: \(2.4\) (not greater than \(5\))
Therefore, the measures that are greater than 5 degrees 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
