Calculating the mean of Soil A:
- Add up all the heights in Soil A:
5 + 5 + 5 + 2 + 1 + 1 + 0 = 19
- Divide by the total number of heights (7):
19 ÷ 7 ≈ 2.71
So the mean height of Teddy Bear sunflowers grown in Soil A is approximately 2.71 cm.
Calculating the mean of Soil B:
- Add up all the heights in Soil B:
6 + 3 + 9 + 7 + 0 + 2 + 3 + 6 + 7 + 8 + 3 + 9 = 63
- Divide by the total number of heights (12):
63 ÷ 12 = 5.25
So the mean height of Teddy Bear sunflowers grown in Soil B is 5.25 cm.
Calculating the MAD of Soil A:
- Find the absolute deviations of each height from the mean:
|5 - 2.71| = 2.29
|5 - 2.71| = 2.29
|5 - 2.71| = 2.29
|2 - 2.71| = 0.71
|1 - 2.71| = 1.71
|1 - 2.71| = 1.71
|0 - 2.71| = 2.71
- Add up all the absolute deviations:
2.29 + 2.29 + 2.29 + 0.71 + 1.71 + 1.71 + 2.71 = 14.41
- Divide by the total number of heights (7):
14.41 ÷ 7 ≈ 2.06
So the MAD of Soil A is approximately 2.06 cm.
Calculating the MAD of Soil B:
- Find the absolute deviations of each height from the mean:
|6 - 5.25| = 0.75
|3 - 5.25| = 2.25
|9 - 5.25| = 3.75
|7 - 5.25| = 1.75
|0 - 5.25| = 5.25
|2 - 5.25| = 3.25
|3 - 5.25| = 2.25
|6 - 5.25| = 0.75
|7 - 5.25| = 1.75
|8 - 5.25| = 2.75
|3 - 5.25| = 2.25
|9 - 5.25| = 3.75
- Add up all the absolute deviations:
0.75 + 2.25 + 3.75 + 1.75 + 5.25 + 3.25 + 2.25 + 0.75 + 1.75 + 2.75 + 2.25 + 3.75 = 29.75
- Divide by the total number of heights (12):
29.75 ÷ 12 ≈ 2.48
So the MAD of Soil B is approximately 2.48 cm.
To determine which set is more variable, we can compare their MAD values. The set with the larger MAD is considered more variable. Therefore, Soil B is more variable than Soil A, since its MAD is larger (2.48 cm vs. 2.06 cm).
ote: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil.
Soil A Soil B
5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
Calculate the mean of each data set.
Calculate the mean absolute deviation (MAD) of each data set.
Which set is more variable? How do you know?.
3 answers
is there an eraser way to do this?
There are different strategies for calculating means and MADs, but they all involve some computation. However, you could use a calculator or spreadsheet software to simplify the calculations and reduce the possibility of errors. For example, you could enter the data of Soil A and B into separate columns or rows, use the built-in functions to calculate the mean and MAD, and get the results in a few clicks. Some calculators also have a STAT mode that allows you to enter data and perform statistics on them without having to do the calculations by hand.
2 answers