Answer:
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:
[tex]x'=\dfrac{2+9+1+3+7+10+2+10+9+7}{10}\\\\x'=\dfrac{60}{10}\\\\x'=6[/tex]
Hence, Mean(x')=6
Now,
∑ |x-x'|=32
Now mean of the absolute deviation is:
[tex]\dfrac{32}{10}=3.2[/tex]
This means that , On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
