Question

the heights, in feet, of the trees for sale at two nurseries are shown below. yard works: 7, 9, 7, 12, 5 the grow station: 9, 11, 6, 12, 7 which statements are true regarding the measures of center and variability of these data sets? select three choices. the mean of the tree heights at yard works is less than the mean of the tree heights at the grow station. the median of the tree heights at yard works is greater than the median of the tree heights at the grow station. the range of the tree heights at yard works is greater than the range of the tree heights at the grow station. the mean absolute deviation of the tree heights at yard works is greater than the mean absolute deviation of the tree heights at the grow station. the mean absolute deviation of the tree heights at yard works is equal to the mean absolute deviation of the tree heights at the grow station.

Explanation:

Step1: Calculate the mean of Yard Works

Mean of Yard Works = $\frac{7 + 9+7 + 12+5}{5}=\frac{40}{5}=8$

Step2: Calculate the mean of The Grow Station

Mean of The Grow Station = $\frac{9 + 11+6 + 12+7}{5}=\frac{45}{5}=9$

Step3: Arrange data of Yard Works for median

Arrange Yard Works data: 5, 7, 7, 9, 12. Median = 7

Step4: Arrange data of The Grow Station for median

Arrange The Grow Station data: 6, 7, 9, 11, 12. Median = 9

Step5: Calculate the range of Yard Works

Range of Yard Works = 12 - 5=7

Step6: Calculate the range of The Grow Station

Range of The Grow Station = 12 - 6 = 6

Step7: Calculate the mean - absolute - deviation of Yard Works

Deviations from mean of Yard Works: |5 - 8|=3, |7 - 8| = 1, |7 - 8| = 1, |9 - 8| = 1, |12 - 8| = 4. Mean absolute deviation of Yard Works=$\frac{3 + 1+1 + 1+4}{5}=\frac{10}{5}=2$

Step8: Calculate the mean - absolute - deviation of The Grow Station

Deviations from mean of The Grow Station: |6 - 9| = 3, |7 - 9| = 2, |9 - 9| = 0, |11 - 9| = 2, |12 - 9| = 3. Mean absolute deviation of The Grow Station=$\frac{3+2 + 0+2+3}{5}=\frac{10}{5}=2$

Answer:

The mean of the tree heights at Yard Works is less than the mean of the tree heights at The Grow Station.
The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station.
The mean absolute deviation of the tree heights at Yard Works is equal to the mean absolute deviation of the tree heights at The Grow Station.