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the following data show the height, in inches, of 11 different garden gnomes:

2 9 1 23 3 7 10 2 10 9 7

after removing the outlier, what does the mean absolute deviation of this data set represent?

a, on average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
b, on average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
c, on average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
d, on average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.

In doing experiments, it is sometime inevitable to commit errors. This is reflected on the set of data points that you have. When you notice that there is an absolute unique point that is very different from the rest, that is the outlier. In this data set, the outlier is 23. You remove the outlier from the data set so as not to significantly affect your results. 

The average or mean, therefore, is

μ = Σx/N = (2+9+1+3+7+10+2+10+9+7)/10
μ = 6

The equation for the mean absolute deviation is

MAD = ∑|x-μ|/N
MAD = [|2-6|+|9-6|+|1-6|+|3-6|+|7-6|+|10-6|+|2-6|+|10-6|+|9-6|+|7-6|]/10
MAD = 3.2

Therefore, the answer is C.

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