Final answer:
The mean absolute deviation (MAD) of the data set 2, 5, 6, 12, 15 is calculated by finding the mean of the set, then computing the absolute deviations from this mean, and finally averaging these deviations. The MAD for this set is 4.4.
Step-by-step explanation:
The question asks how to find the mean absolute deviation (MAD) for the data set 2, 5, 6, 12, 15. To compute MAD, first, calculate the mean (average) of the data set, then find the absolute deviations from this mean (the absolute value of the differences between each data point and the mean), and finally, calculate the average of those absolute deviations.
Steps to compute the MAD:
- Find the mean of the data set by adding all data points and dividing by the number of points: (2+5+6+12+15) / 5 = 40 / 5 = 8.
- Calculate the absolute deviations: |2-8| = 6, |5-8| = 3, |6-8| = 2, |12-8| = 4, and |15-8| = 7.
- Find the mean of these absolute deviations: (6+3+2+4+7) / 5 = 22 / 5 = 4.4.
The mean absolute deviation of the data set is 4.4.