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

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

**Step 1: Calculate the MAD for Set 1.**

Set 1: 16, 15, 10, 12

1. Find the mean of Set 1:
\[
\text{Mean} = \frac{16 + 15 + 10 + 12}{4} = \frac{53}{4} = 13.25
\]

2. Calculate the absolute deviations from the mean:
- |16 - 13.25| = 2.75
- |15 - 13.25| = 1.75
- |10 - 13.25| = 3.25
- |12 - 13.25| = 1.25

3. Calculate the mean of these absolute deviations:
\[
\text{MAD} = \frac{2.75 + 1.75 + 3.25 + 1.25}{4} = \frac{9}{4} = 2.25
\]

**Step 2: Calculate the MAD for Set 2.**

Set 2: 16, 62, 15, 10, 12

1. Find the mean of Set 2:
\[
\text{Mean} = \frac{16 + 62 + 15 + 10 + 12}{5} = \frac{115}{5} = 23
\]

2. Calculate the absolute deviations from the mean:
- |16 - 23| = 7
- |62 - 23| = 39
- |15 - 23| = 8
- |10 - 23| = 13
- |12 - 23| = 11

3. Calculate the mean of these absolute deviations:
\[
\text{MAD} = \frac{7 + 39 + 8 + 13 + 11}{5} = \frac{78}{5} = 15.6
\]

**Step 3: Compare the MAD of Set 1 and Set 2.**

From our calculations:
- MAD of Set 1 = 2.25
- MAD of Set 2 = 15.6

Now, let's find the difference:
\[
\text{Difference} = \text{MAD of Set 2} - \text{MAD of Set 1} = 15.6 - 2.25 = 13.35
\]

Thus, the MAD of Set 2 is **13.35 more than the MAD of Set 1.**

So, the correct answer is:
**The MAD of set 2 is 13.35 more than the MAD of set 1.**