Question

How does the mean absolute deviation (MAD) of the data in set 2 compare to the mean absolute deviation of the data in set 1? Set 1: 16, 15, 10, 12 Set 2: 16, 62, 15, 10, 12 The MAD of set 2 is 10 less than the MAD of set 1. The MAD of set 2 is 13. 35 more than the MAD of set 1. The MAD of set 2 is 10 more than the MAD of set 1. The MAD of set 2 is 13. 35 less than the MAD of set 1.

Answer 1

The MAD of set 2 is 13. 35 more than the MAD of set 1.

What is Mean absolute deviation?

The average distance between each data point and the mean is the mean absolute deviation of a dataset.

The mean of the first data set is,

$\rm Mean_1=\dfrac{16+ 15+ 10+ 12}{4} = 13.25$

Now, the mean absolute deviation of the first data set is,

$\rm MAD_1=\dfrac{2.75+ 1.75+ 3.25+ 1.25}{4} = 2.25$

The mean of the second data set is,

$\rm Mean_2=\dfrac{16+ 62+ 15+10+ 12}{5} = 23$

Now, the mean absolute deviation of the second data set is,

$\rm MAD_2=\dfrac{7+39+8+13+11}{5} = 15.6$

Now, if we calculate the difference in the mean absolute deviation of the two sets, therefore, the difference in the MAD is,

$\text{Difference in MAD}=MAD_2-MAD_1 = 15.6-2.25 = 13.35$

Hence, The MAD of set 2 is 13. 35 more than the MAD of set 1.

Learn more about MAD:

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