Question

How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?

Set 1: 12, 8, 10, 50
Set 2: 13, 9, 8
The MAD of set 1 is 13 less than the MAD of set 2.
The MAD of set 1 is 13 more than the MAD of set 2.
The MAD of set 1 is 2 more than the MAD of set 2.
The MAD of set 1 is 2 less than the MAD of set 2.

Answer 1

To compare the mean absolute deviation (MAD) of the two sets, we need to calculate the MAD for each set.

**Step 1: Calculate the Mean and MAD for Set 1 (12, 8, 10, 50)**

1. Find the mean of Set 1:
\[
\text{Mean} = \frac{12 + 8 + 10 + 50}{4} = \frac{80}{4} = 20
\]

2. Calculate the absolute deviations from the mean:
- |12 - 20| = 8
- |8 - 20| = 12
- |10 - 20| = 10
- |50 - 20| = 30

3. Find the mean of these absolute deviations (MAD):
\[
\text{MAD}_{1} = \frac{8 + 12 + 10 + 30}{4} = \frac{60}{4} = 15
\]

**Step 2: Calculate the Mean and MAD for Set 2 (13, 9, 8)**

1. Find the mean of Set 2:
\[
\text{Mean} = \frac{13 + 9 + 8}{3} = \frac{30}{3} = 10
\]

2. Calculate the absolute deviations from the mean:
- |13 - 10| = 3
- |9 - 10| = 1
- |8 - 10| = 2

3. Find the mean of these absolute deviations (MAD):
\[
\text{MAD}_{2} = \frac{3 + 1 + 2}{3} = \frac{6}{3} = 2
\]

**Step 3: Compare the MADs**

- MAD of Set 1: 15
- MAD of Set 2: 2

Now we compare the two:
\[
\text{MAD}_{1} - \text{MAD}_{2} = 15 - 2 = 13
\]

Thus, the MAD of Set 1 is 13 more than the MAD of Set 2.

The correct statement is:
**The MAD of set 1 is 13 more than the MAD of set 2.**