Question

Find and interpret the mean absolute deviation of the data. $4.6,8.5,7.2,6.6,5.1,6.2,8.1,10.3$ The mean absolute deviation is . The values differ from the mean by an average of .

Answer 1

Using it's concept, it is found that:

- The mean absolute deviation is 1.45.

- The values differ from the mean by an average of 1.45.

What is the mean absolute deviation of a data-set?

- The mean of a data-set is given by the sum of all observations divided by the number of observations.

- The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.

- The mean absolute deviation represents the average by which the values differ from the mean.

In this problem, the mean of the data-set is given by:

M = (4.6 + 8.5 + 7.2 + 6.6 + 5.1 + 6.2 + 8.1 + 10.3)/8 = 7.075.

Hence, the mean absolute deviation is given by:

MAD = (|4.6-7.075| + |8.5-7.075| + |7.2-7.075| + |6.6-7.075| + |5.1-7.075| + |6.2-7.075| + |8.1-7.075| + |10.3-7.075|)/8 = 1.45

Then:

- The mean absolute deviation is 1.45.

- The values differ from the mean by an average of 1.45.

More can be learned about the mean absolute deviation at