Mean for Soil A: 51.2 cm
Mean for Soil B: 67.2 cm
To calculate MAD, we first need to find the absolute deviations for each data point from the respective mean:
For Soil A:
- 51.2 - 21 = 30.2
- 51.2 - 20 = 31.2
- 51.2 - 50 = 1.2
- 51.2 - 59 = 7.8
- 51.2 - 51 = 0.2
- 51.2 - 50 = 1.2
- 51.2 - 23 = 28.2
- 51.2 - 30 = 21.2
- 51.2 - 39 = 12.2
- 51.2 - 31 = 20.2
- 51.2 - 32 = 19.2
- 51.2 - 38 = 13.2
- 51.2 - 44 = 7.2
- 51.2 - 43 = 8.2
- 51.2 - 44 = 7.2
- 51.2 - 33 = 18.2
- 51.2 - 34 = 17.2
- 51.2 - 32 = 19.2
MAD for Soil A: (30.2 + 31.2 + 1.2 + 7.8 + 0.2 + 1.2 + 28.2 + 21.2 + 12.2 + 20.2 + 19.2 + 13.2 + 7.2 + 8.2 + 7.2 + 18.2 + 17.2 + 19.2) / 18 ≈ 14.17 cm
For Soil B:
- 67.2 - 69 = 1.8
- 67.2 - 63 = 4.2
- 67.2 - 68 = 0.8
- 67.2 - 70 = 2.8
- 67.2 - 69 = 1.8
- 67.2 - 62 = 5.2
- 67.2 - 60 = 7.2
- 67.2 - 67 = 0.2
- 67.2 - 68 = 0.8
- 67.2 - 69 = 1.8
- 67.2 - 61 = 6.2
- 67.2 - 63 = 4.2
- 67.2 - 63 = 4.2
- 67.2 - 64 = 3.2
- 67.2 - 64 = 3.2
- 67.2 - 64 = 3.2
- 67.2 - 65 = 2.2
- 67.2 - 66 = 1.2
MAD for Soil B: (1.8 + 4.2 + 0.8 + 2.8 + 1.8 + 5.2 + 7.2 + 0.2 + 0.8 + 1.8 + 6.2 + 4.2 + 4.2 + 3.2 + 3.2 + 3.2 + 2.2 + 1.2) / 18 ≈ 2.94 cm
Soil A is more variable as its data points have a larger range of values and a higher MAD compared to Soil B.
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
3 answers
can you just give me the answer not the equation
Sure, the mean for Soil A is 51.2 cm and the mean for Soil B is 67.2 cm. The MAD for Soil A is approximately 14.17 cm and the MAD for Soil B is approximately 2.94 cm. Soil A is more variable than Soil B.