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| 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. Key: 5|8 means
69. 58
Calculate the (MAD) of each data set
To calculate the MAD of each data set, we will first need to compute the residual (deviation from the median) of each data point, then take the absolute value of each residual, and finally find the median of all the absolute residuals.
Here are the steps we can follow:
For the first data set:
- Median: 6
- Residuals:
- |-1-6| = 7
- |3-6| = 3
- |9-6| = 3
- Absolute residuals: 7, 3, 3
- MAD: median(7, 3, 3) = 3
Therefore, the MAD of the first data set is 3.
For the second data set:
- Median: 5
- Residuals:
- |3-5| = 2
- |6-5| = 1
- |7-5| = 2
- |0-5| = 5
- |2-5| = 3
- |3-5| = 2
- |6-5| = 1
- |7-5| = 2
- |8-5| = 3
- Absolute residuals: 2, 1, 2, 5, 3, 2, 1, 2, 3
- MAD: median(2, 1, 2, 5, 3, 2, 1, 2, 3) = 2
Therefore, the MAD of the second data set is 2.
Which set is more variable
To determine which set is more variable, we can compare the MADs of the two sets. The data set with the larger MAD is more variable, since the MAD is a measure of variability that takes into account the absolute distance of each data point from the median.
Using the MADs we calculated earlier, we have:
- MAD of first data set: 3
- MAD of second data set: 2
Since the MAD of the first data set is larger than the MAD of the second data set, we conclude that the first data set is more variable.
Calculate the mean of each data set
To calculate the mean of each data set, we need to sum up all the data points in the set and divide by the number of data points. Here are the calculations:
For the first data set:
- Sum of data points: 1 + 1 + 2 + 3 + 5 + 5 + 9 = 26
- Number of data points: 7
- Mean: 26 / 7 = 3.71 (rounded to two decimal places)
Therefore, the mean of the first data set is 3.71.
For the second data set:
- Sum of data points: 0 + 1 + 2 + 3 + 5 + 6 + 7 + 8 + 9 = 41
- Number of data points: 9
- Mean: 41 / 9 = 4.56 (rounded to two decimal places)
Therefore, the mean of the second data set is 4.56.