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
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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a) To describe the overlap of the two sets of data, we need to compare the heights in centimeters of Teddy Bear sunflowers grown in Soil A and Soil B. Looking at the stem-and-leaf plot, we can see that both datasets have heights ranging from the 50s to the 90s. However, Soil A has more values in the 50s and 60s, while Soil B has more values in the 70s and 80s. There is a slight overlap in the 70s, where both datasets have values. Overall, there is some overlap in the middle range of heights, but the datasets also have distinct values unique to each soil type.
b) To calculate the mean of each dataset, we need to find the average height in centimeters for Soil A and Soil B. In Soil A, we have the following values: 51, 52, 55, 61, 67, 68, 69, 70, 79, and 92. Adding these values together, we get a sum of 624. Dividing this sum by the number of values (10), we find that the mean height for Soil A is 62.4 centimeters.
In Soil B, we have the following values: 59, 60, 63, 63, 67, 70, 72, 73, 78, 79, 84, 87, 89, and 90. Adding these values together, we get a sum of 1024. Dividing this sum by the number of values (14), we find that the mean height for Soil B is approximately 73.14 centimeters.
c) To calculate the mean absolute deviation (MAD) of each dataset, we need to find the average distance from the mean for each value in the dataset.
For Soil A, we will use the mean we calculated earlier (62.4) and find the absolute value of the difference between each value and the mean. Then, we calculate the sum of these absolute differences and divide it by the number of values (10). This gives us the MAD for Soil A.
For Soil B, we will use the mean we calculated earlier (73.14) and follow the same process to find the MAD for Soil B.
d) To determine which set is more variable, we compare the MAD of each dataset. The dataset with a higher MAD is considered to be more variable because it indicates that the values in that dataset are more spread out from the mean. By comparing the MAD of Soil A and Soil B, we can determine which dataset is more variable.