Soil A Soil B
5 9
5221 6 3 9
510 7 0 2 3 6 7 8
21 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
A. Calculate the mean of each data set.
B. Calculate the mean absolute deviation (MAD) of each data set.
C. Which set is more variable? How do you know?
omg the chart is all messed up
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
To calculate the mean and mean absolute deviation (MAD) for each data set, follow these steps:
A. Calculate the mean:
1. For Soil A, add up all the numbers: 5 + 6 + 7 + 8 + 9 + 21 + 510 + 5221 = 5797.
2. Divide the sum by the number of values in the data set (in this case, there are 8 values): 5797 / 8 = 724.625. So, the mean for Soil A is approximately 724.625.
3. For Soil B, add up all the numbers: 9 + 3 + 0 + 2 + 3 + 6 + 7 + 8 + 9 = 47.
4. Divide the sum by the number of values in the data set (in this case, there are 9 values): 47 / 9 ≈ 5.222. So, the mean for Soil B is approximately 5.222.
B. Calculate the mean absolute deviation (MAD):
1. Calculate the absolute deviation for each data point. To do this, subtract the mean from each data point and take the absolute value.
- For Soil A:
- Absolute deviation for 5: |5 - 724.625| ≈ 719.625
- Absolute deviation for 6: |6 - 724.625| ≈ 718.625
- Absolute deviation for 7: |7 - 724.625| ≈ 717.625
- Absolute deviation for 8: |8 - 724.625| ≈ 716.625
- Absolute deviation for 9: |9 - 724.625| ≈ 715.625
- Absolute deviation for 21: |21 - 724.625| ≈ 703.625
- Absolute deviation for 510: |510 - 724.625| ≈ 214.625
- Absolute deviation for 5221: |5221 - 724.625| ≈ 4496.375
2. For Soil A, add up all the absolute deviations: 719.625 + 718.625 + 717.625 + 716.625 + 715.625 + 703.625 + 214.625 + 4496.375 ≈ 5556.125.
3. Divide the sum by the number of values in the data set (in this case, there are 8 values): 5556.125 / 8 ≈ 694.516. So, the MAD for Soil A is approximately 694.516.
4. Repeat steps 1-3 for Soil B:
- For Soil B:
- Absolute deviation for 9: |9 - 5.222| ≈ 3.778
- Absolute deviation for 3: |3 - 5.222| ≈ 2.222
- Absolute deviation for 0: |0 - 5.222| ≈ 5.222
- Absolute deviation for 2: |2 - 5.222| ≈ 3.222
- Absolute deviation for 3: |3 - 5.222| ≈ 2.222
- Absolute deviation for 6: |6 - 5.222| ≈ 0.778
- Absolute deviation for 7: |7 - 5.222| ≈ 1.778
- Absolute deviation for 8: |8 - 5.222| ≈ 2.778
- Absolute deviation for 9: |9 - 5.222| ≈ 3.778
5. Add up all the absolute deviations: 3.778 + 2.222 + 5.222 + 3.222 + 2.222 + 0.778 + 1.778 + 2.778 + 3.778 ≈ 25.778.
6. Divide the sum by the number of values in the data set (in this case, there are 9 values): 25.778 / 9 ≈ 2.864. So, the MAD for Soil B is approximately 2.864.
C. To determine which set is more variable, compare the MAD for each data set. The data set with a larger MAD is more variable. In this case, Soil A has a MAD of approximately 694.516, while Soil B has a MAD of approximately 2.864. Comparing these values, Soil A has a much higher MAD, indicating greater variability compared to Soil B. Therefore, Soil A is more variable.