A 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
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?
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Help with this homework
a) To describe the overlap of the two sets of data, we can examine the stem-and-leaf plot. The stem-and-leaf plot shows the heights of Teddy Bear sunflowers grown in Soil A and Soil B. By comparing the stems in both data sets, we can identify the common values or the "overlap" between the two sets.
Looking at the stems 5, 6, 7, 8, and 9, we can see that both Soil A and Soil B have data points in these stems. For example, in stem 5, both Soil A and Soil B have values of 5, 5, and 5. Similarly, in stem 9, both Soil A and Soil B have values of 9. This indicates that there is an overlap of data points between the two sets.
b) To calculate the mean of each data set, we need to find the average height for Soil A and Soil B. To do this, we add up all the data points in each set and divide by the total number of data points.
For Soil A:
Mean = (5 + 2 + 1 + 1 + 5 + 1 + 0 + 2 + 1 + 8 + 3 + 9 + 0) / 13
For Soil B:
Mean = (9 + 6 + 3 + 9 + 7 + 0 + 2 + 3 + 6 + 7 + 8 + 3) / 12
By performing these calculations, we can find the mean of each data set.
c) To calculate the mean absolute deviation (MAD) of each data set, we need to find the average distance between each data point and the mean of the respective data set. Here's how to calculate MAD:
For Soil A:
1. Find the mean of Soil A (as calculated in part b).
2. Subtract the mean from each data point to find the deviations.
3. Take the absolute value of each deviation.
4. Find the mean of these absolute deviations.
Repeat the steps for Soil B to find the MAD of that data set as well.
d) To determine which set is more variable, we can compare the mean absolute deviations (MAD) of Soil A and Soil B. If one set has a higher MAD, it indicates greater variability in the data.
By comparing the MADs calculated in part c, we can determine which set is more variable. A higher MAD means more variability in the data, while a lower MAD means less variability. Hence, we can analyze the MADs of Soil A and Soil B to identify which set is more variable.