Question

What is the mean absolute deviation of the following set of data?
4, 2, 2, 10

Answer 1

The mean absolute deviation (MAD) of the given data set is 2.75.

Explanation:

Mean Absolute Deviation (MAD) is a way to measure how spread out a set of numbers is from their mean. A smaller MAD means the numbers are closer to the mean, while a larger MAD means they are more spread out.

To find the mean absolute deviation (MAD) of a set of data, first calculate the mean of the data set.

To find the mean, divide the sum of the data by the number of data points:

`\textsf{Mean}=(4+2+2+10)/(4)=(18)/(4)=4.5`

Therefore, the mean is 4.5.

Now calculate the absolute difference between each data point and the mean:

`|4 - 4.5| = |-0.5| = 0.5`

`|2 - 4.5| = |-2.5|=2.5`

`|2 - 4.5| = |-2.5|=2.5`

`|10 - 4.5| = |5.5|=5.5`

Finally, calculate the mean of the absolute differences by dividing the sum of the absolute differences by the number of data points:

`\textsf{M.A.D.}=(0.5+2.5+2.5+5.5)/(4)=(11)/(4)=2.75`

Therefore, the mean absolute deviation (MAD) of the given data set is 2.75.