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
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.
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.
To calculate the mean of each dataset, we need to add up all the values in each dataset and then divide by the total number of values.
For Soil A:
The values in Soil A are: 55, 52, 51, 56, 53, 59, 50, 58, 58, 59, 51, 53, 50, 51, 58, 57, 58, 50
Adding them all up, we get: 945
There are 18 values in Soil A.
Dividing 945 by 18, we get the mean of Soil A: 52.5
For Soil B:
The values in Soil B are: 96, 93, 90, 92, 93, 96, 97, 98, 93, 90, 99
Adding them all up, we get: 950
There are 11 values in Soil B.
Dividing 950 by 11, we get the mean of Soil B: 86.4
Now, let's calculate the mean absolute deviation (MAD) of each dataset.
To calculate the MAD, we first need to find the absolute deviation of each value from the mean. Then, we add up all the absolute deviations and divide by the total number of values.
For Soil A:
The mean of Soil A is 52.5.
The absolute deviations of each value from the mean are:
2.5, 0.5, 1.5, 3.5, 0.5, 6.5, 2.5, 5.5, 5.5, 6.5, 0.5, 2.5, 2.5, 1.5, 5.5, 4.5, 5.5, 2.5
Adding them all up, we get: 64
There are 18 values in Soil A.
Dividing 64 by 18, we get the MAD of Soil A: 3.6
For Soil B:
The mean of Soil B is 86.4.
The absolute deviations of each value from the mean are:
9.6, 6.4, 4.4, 5.6, 6.4, 9.6, 10.6, 11.6, 6.4, 4.4, 12.6
Adding them all up, we get: 92.8
There are 11 values in Soil B.
Dividing 92.8 by 11, we get the MAD of Soil B: 8.4
To determine which set is more variable, we compare the MADs of the two datasets. The dataset with a larger MAD is considered more variable.
In this case, Soil B has a MAD of 8.4, while Soil A has a MAD of 3.6. Therefore, Soil B is more variable because it has a larger MAD.