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: 5, 10, 7, 2
Set 2: 5, 10, 7, 42
The MAD of set 1 is 10.5 more than the MAD of set 2.
The MAD of set 1 is 2.5 more than the MAD of set 2.
The MAD of set 1 is 10.5 less than the MAD of set 2.
The MAD of set 1 is 2.5 less than the MAD of set 2.

Answer 1

To compare the Mean Absolute Deviation (MAD) of Set 1 and Set 2, we need to calculate the MAD for both sets.

**Set 1: 5, 10, 7, 2**
1. Calculate the mean:
\[
\text{Mean} = \frac{5 + 10 + 7 + 2}{4} = \frac{24}{4} = 6
\]

2. Calculate the absolute deviations from the mean:
- |5 - 6| = 1
- |10 - 6| = 4
- |7 - 6| = 1
- |2 - 6| = 4

3. Calculate the mean of those absolute deviations (MAD):
\[
\text{MAD} = \frac{1 + 4 + 1 + 4}{4} = \frac{10}{4} = 2.5
\]

**Set 2: 5, 10, 7, 42**
1. Calculate the mean:
\[
\text{Mean} = \frac{5 + 10 + 7 + 42}{4} = \frac{64}{4} = 16
\]

2. Calculate the absolute deviations from the mean:
- |5 - 16| = 11
- |10 - 16| = 6
- |7 - 16| = 9
- |42 - 16| = 26

3. Calculate the mean of those absolute deviations (MAD):
\[
\text{MAD} = \frac{11 + 6 + 9 + 26}{4} = \frac{52}{4} = 13
\]

**Comparison:**
- MAD of Set 1 = 2.5
- MAD of Set 2 = 13

Now to compare them:
\[
\text{MAD of Set 1} (2.5) < \text{MAD of Set 2} (13)
\]

To find the difference:
\[
\text{Difference} = 13 - 2.5 = 10.5
\]

So, we find that:
The MAD of set 1 is 10.5 less than the MAD of set 2.

Thus, the correct answer is:
**The MAD of set 1 is 10.5 less than the MAD of set 2.**