Final answer:
The mean absolute deviation (MAD) is a good indicator of variation when the data set is fairly close to one another. In the given data set (2, 9, 19, 22, 25, 26, 44), the MAD is approximately 9.43.
Step-by-step explanation:
The mean absolute deviation (MAD) is a good indicator of variation of the data when the data set is fairly close to one another. In other words, if the data values are concentrated closely near the mean, the MAD would be a good measure of variation.
In the given data set, the values are:
2, 9, 19, 22, 25, 26, 44
To calculate the MAD, we first need to find the mean of the data set:
(2 + 9 + 19 + 22 + 25 + 26 + 44) / 7 = 147 / 7 = 21
Next, we find the absolute deviation of each value from the mean:
|2 - 21| = 19
|9 - 21| = 12
|19 - 21| = 2
|22 - 21| = 1
|25 - 21| = 4
|26 - 21| = 5
|44 - 21| = 23
Then, we find the mean of these absolute deviations:
(19 + 12 + 2 + 1 + 4 + 5 + 23) / 7 = 66 / 7 ≈ 9.43
Therefore, the MAD for the given data set is approximately 9.43. Since the values are not too spread out and are fairly close to the mean, the MAD can be a good indicator of their variation.