Question

Determine the mean absolute deviation (MAD) of the following dataset. Round your answer to the nearest tenth.



11.2, 13.7, 15.1, 17.5, 18.2, 19.1

Answer 1

To calculate the mean absolute deviation (MAD) of the dataset, follow these steps:

1. **Calculate the mean** of the dataset.
2. **Find the absolute deviations** from the mean for each data point.
3. **Calculate the mean** of these absolute deviations.

Let's start with the dataset:

\[ 11.2, 13.7, 15.1, 17.5, 18.2, 19.1 \]

### Step 1: Calculate the Mean

The mean (\(\bar{x}\)) is calculated as follows:

\[
\bar{x} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]

\[
\text{Sum} = 11.2 + 13.7 + 15.1 + 17.5 + 18.2 + 19.1 = 94.8
\]

\[
\text{Number of data points} = 6
\]

\[
\bar{x} = \frac{94.8}{6} \approx 15.8
\]

### Step 2: Find the Absolute Deviations from the Mean

Next, we need to calculate the absolute deviations of each data point from the mean \(15.8\):

\[
|11.2 - 15.8| = | -4.6| = 4.6
\]
\[
|13.7 - 15.8| = |-2.1| = 2.1
\]
\[
|15.1 - 15.8| = |-0.7| = 0.7
\]
\[
|17.5 - 15.8| = | 1.7| = 1.7
\]
\[
|18.2 - 15.8| = | 2.4| = 2.4
\]
\[
|19.1 - 15.8| = | 3.3| = 3.3
\]

So the absolute deviations are:

\[ 4.6, 2.1, 0.7, 1.7, 2.4, 3.3 \]

### Step 3: Calculate the Mean of the Absolute Deviations

Now, calculate the mean of these absolute deviations:

\[
\text{Sum of absolute deviations} = 4.6 + 2.1 + 0.7 + 1.7 + 2.4 + 3.3 = 14.8
\]

\[
\text{Mean of absolute deviations} = \frac{14.8}{6} \approx 2.46666667
\]

Rounding this to the nearest tenth:

\[
\text{MAD} \approx 2.5
\]

Therefore, the mean absolute deviation (MAD) of the dataset is approximately \( \boxed{2.5} \).