Question

What is the mean absolute deviation for the set of data below?

2, 8, 10, 16

Answer 1

To find the mean absolute deviation (MAD) for the set of data \( 2, 8, 10, 16 \), follow these steps:

1. **Calculate the mean** of the data set.
2. **Determine the absolute deviations** from the mean.
3. **Calculate the mean of those absolute deviations**.

### Step 1: Calculate the Mean

The mean (average) is calculated by summing all the data points and dividing by the number of points:

\[
\text{Mean} = \frac{2 + 8 + 10 + 16}{4} = \frac{36}{4} = 9
\]

### Step 2: Calculate Absolute Deviations

Now, we find the absolute deviations from the mean (9):

- For \( 2 \): \( |2 - 9| = | -7 | = 7 \)
- For \( 8 \): \( |8 - 9| = | -1 | = 1 \)
- For \( 10 \): \( |10 - 9| = | 1 | = 1 \)
- For \( 16 \): \( |16 - 9| = | 7 | = 7 \)

### Step 3: Mean of Absolute Deviations

Now, we calculate the mean of these absolute deviations:

\[
\text{Mean Absolute Deviation} = \frac{7 + 1 + 1 + 7}{4} = \frac{16}{4} = 4
\]

Thus, the mean absolute deviation for the set of data \( 2, 8, 10, 16 \) is \(\boxed{4}\).