Answer :
Answer:
Step-by-step explanation:
Finding the Mean Absolute Deviation (MAD)
Here's how to find the mean absolute deviation (MAD) for the volunteer hours data set:
Calculate the mean:
Add all the volunteer hours and divide by the number of students (n):
Mean = (1 + 1 + 2 + 2 + 4 + 5 + 6 + 7 + 8 + 9) / 10 = 4.5 hours
Find the absolute deviations from the mean:
For each student, calculate the absolute difference between their volunteer hours and the mean.
Student Volunteer Hours Deviation from Mean Absolute Deviation
1 1 hour -3.5 hours 3.5 hours
2 1 hour -3.5 hours 3.5 hours
3 2 hours -2.5 hours 2.5 hours
4 2 hours -2.5 hours 2.5 hours
5 4 hours -0.5 hours 0.5 hours
6 5 hours 0.5 hours 0.5 hours
7 6 hours 1.5 hours 1.5 hours
8 7 hours 2.5 hours 2.5 hours
9 8 hours 3.5 hours 3.5 hours
10 9 hours 4.5 hours 4.5 hours
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Calculate the mean absolute deviation (MAD):
Add the absolute deviations from step 2 and divide by the number of students (n):
MAD = (3.5 + 3.5 + 2.5 + 2.5 + 0.5 + 0.5 + 1.5 + 2.5 + 3.5 + 4.5) / 10
MAD = 30 / 10 = 3.0 hours
Interpretation:
The mean absolute deviation (MAD) of 3.0 hours indicates that, on average, volunteer hours deviate from the average time commitment (4.5 hours) by 3.0 hours. In other words, most students volunteered within 3 hours of the average time commitment.
Note:
MAD is a robust measure of spread compared to standard deviation because it is less sensitive to outliers. It provides a good idea of how spread out the data is from the mean.
