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?
I really need help with it.
you like a senior now
a) To describe the overlap of the two sets of data in the stem-and-leaf plot, we need to compare the values in each stem. Looking at the plot, we can see that both Soil A and Soil B have some overlapping values in the same stems. For example, both Soil A and Soil B have a value of 5 in the stem "5|", and they also have a value of 9 in the stem "9|". This indicates that there are some sunflowers of the same height in both Soil A and Soil B.
b) To calculate the mean of each data set, we need to find the sum of all the values in the data set and divide it by the total number of values. For Soil A, we have the following values: 59, 56, 539, 27, 023678, 19. Summing these values, we get 1523. Since there are 6 values in Soil A, the mean can be calculated as 1523/6 = 253.8.
For Soil B, we have the following values: 58, 69, 67, 023678, 83, 9. Summing these values, we get 309. Since there are 6 values in Soil B, the mean can be calculated as 309/6 = 51.5.
c) To calculate the mean absolute deviation (MAD) of each data set, we need to find the absolute difference between each value and the mean, sum these absolute differences, and divide by the total number of values.
For Soil A, the mean was calculated to be 253.8. The absolute differences between each value and the mean are as follows: 194.8, 197.8, 286.8, 226.8, 229.8, 234.8. Summing these absolute differences, we get 1370.8. Since there are 6 values in Soil A, the MAD can be calculated as 1370.8/6 = 228.47.
For Soil B, the mean was calculated to be 51.5. The absolute differences between each value and the mean are as follows: 6.5, 17.5, 15.5, 27.5, 31.5, 41.5. Summing these absolute differences, we get 140. Similarly, as there are 6 values in Soil B, the MAD can be calculated as 140/6 = 23.33.
d) To determine which set is more variable, we can compare the mean absolute deviations (MADs) of both data sets. The set with the larger MAD is more variable.
In this case, Soil A has a MAD of 228.47, while Soil B has a MAD of 23.33. Since the MAD of Soil A is significantly larger than the MAD of Soil B, we can conclude that Soil A is more variable. The larger MAD indicates greater dispersion of data points from the mean in Soil A compared to Soil B.