Final answer:
To find the mean absolute deviation (MAD) for the data set, calculate the mean, subtract it from each data value to find deviations, take the absolute values, and then find their mean. The MAD for the data set 12, 17, 16, 9, 18, 10, 9 is approximately 3.43.
Step-by-step explanation:
To find the mean absolute deviation (MAD) for a given data set, we follow these steps:
Calculate the mean (average) of the data set.
Subtract the mean from each data value to find the deviations.
Take the absolute value of each deviation.
Find the average of these absolute values to determine the MAD.
The data set provided is: 12, 17, 16, 9, 18, 10, 9. First, let's calculate the mean:
(12 + 17 + 16 + 9 + 18 + 10 + 9) / 7 = 91 / 7 = 13
Next, we'll find the absolute deviations from the mean:
|12 - 13| = 1
|17 - 13| = 4
|16 - 13| = 3
|9 - 13| = 4
|18 - 13| = 5
|10 - 13| = 3
|9 - 13| = 4
Lastly, we calculate the mean of these absolute values:
(1 + 4 + 3 + 4 + 5 + 3 + 4) / 7 = 24 / 7 ≈ 3.43
The mean absolute deviation of the data set is approximately 3.43.