Question

The following data show the height, in inches, of 11 different plants in a garden: 9 4 10 9 5 2 22 10 3 3 5 After removing the outlier, what does the mean absolute deviation of this data set represent?

Answer 1

I took the test, it is On average, the height of a plant varies 2.8 inches from the mean of 6 inches.

Explanation:

Answer 2

The outlier is the obviously different data among the whole group of data points. In this case, the outlier is 22. When you find the mean, you only use the data points without the outlier. Therefore,

Mean = (9+4+10+9+5+2+10+3+3+5)/10 = 6

Then, the mean absolute deviation is

∑(x-mean)^2/n, where x is every single data point and n is the number of data points which is equal to 10

|9-6|+|4-6|+|10-6|+|9-6|+|5-6|+|2-6|+|10-6|+|3-6|+|3-6|+|5-6| = 28

Then,

Mean Absolute Deviation (MAD) = 28/10 = 2.8

This is the average distance of the data from the mean.