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 | 39
510 | 7 | 023678
21| 8 | 3
0| 9
Key: 9|6 means 69,Key: 5|8 means 58
a) Describe the overlap of the two sets of data.
b) Calculate the mean of each data set.
c) Calculate the mean absolute deviation (MAD) of each data set.
d) Which set is more variable? How do you know?
Can some one show me steps how to do this
Says the person who cant spell stupid.
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a) To describe the overlap of the two sets of data in the given stem-and-leaf plot, you need to compare the numbers represented in both Soil A and Soil B. Look for common numbers or stems with corresponding leaves. Based on the given plot, we can observe the following overlap:
- Soil A: The data includes heights of 51, 52, 56, 59, 59, and 60.
- Soil B: The data includes heights of 23, 26, 27, 28, 30, 36, 37, 38, and 39.
Therefore, the overlap between the two sets of data is the height 59, which is present in both Soil A and Soil B.
b) To calculate the mean of each data set, you need to find the average of the given data points.
- Soil A mean: (51 + 52 + 56 + 59 + 59 + 60) / 6 = 337 / 6 = 56.17 cm
- Soil B mean: (23 + 26 + 27 + 28 + 30 + 36 + 37 + 38 + 39) / 9 = 304 / 9 = 33.78 cm
Therefore, the mean of Soil A is approximately 56.17 cm, and the mean of Soil B is approximately 33.78 cm.
c) To calculate the mean absolute deviation (MAD) of each data set, you need to find the average distance between each data point and the mean.
- Soil A MAD: Subtract the mean from each data point, take the absolute value, sum the values, and then divide by the number of data points.
MAD = [(51 - 56.17) + (52 - 56.17) + (56 - 56.17) + (59 - 56.17) + (59 - 56.17) + (60 - 56.17)] / 6
= [(-5.17) + (-4.17) + (-0.17) + (2.83) + (2.83) + (3.83)] / 6
= (-1.50) / 6
= 0.25 cm
- Soil B MAD: Subtract the mean from each data point, take the absolute value, sum the values, and then divide by the number of data points.
MAD = [(23 - 33.78) + (26 - 33.78) + (27 - 33.78) + (28 - 33.78) + (30 - 33.78) + (36 - 33.78) + (37 - 33.78) + (38 - 33.78) + (39 - 33.78)] / 9
= [(-10.78) + (-7.78) + (-6.78) + (-5.78) + (-3.78) + (2.22) + (3.22) + (4.22) + (5.22)] / 9
= (-7.59) / 9
= 0.84 cm
Therefore, the MAD of Soil A is approximately 0.25 cm, and the MAD of Soil B is approximately 0.84 cm.
d) To determine which set is more variable, you can compare the MAD values calculated in the previous step. The set with a higher MAD is more variable because it indicates larger deviations from the mean. In this case, Soil B has a higher MAD (0.84 cm) compared to Soil A (0.25 cm), which implies that Soil B is more variable.