(08.06)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?
on average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
on average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
on average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
on average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.

The correct statement is:

On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.

Step-by-step explanation:

We are given a data of 11 gardens as:

2   9    1    23    3    7    10    2    10    9     7

Now on removing the outlier i.e. 23 (since it is the very large value as compared to other data points) the entries are as follows:

x         |x-x'|        

2          4              

9          3              

1           5              

3          3              

7           1                

10         4              

2           4              

10          4              

9           3              

7            1              

Now mean of the data is denoted by x' and is calculated as:

Hence, Mean(x')=6

Now,

∑ |x-x'|=32

Now mean of the absolute deviation is:

This means that , On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.

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