Question

Find the mean absolute deviation of the following dataset. Express your answer as a decimal.

{21,25,25,26,26,27,28,30}

Answer 1

To find the mean absolute deviation (MAD) of the dataset \(\{21, 25, 25, 26, 26, 27, 28, 30\}\), we can follow these steps:

1. **Calculate the mean of the dataset:**

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

Calculating the sum:

\[
21 + 25 + 25 + 26 + 26 + 27 + 28 + 30 = 208
\]

The number of data points is \(8\). Thus, the mean is:

\[
\text{Mean} = \frac{208}{8} = 26
\]

2. **Calculate the absolute deviations from the mean:**

For each data point, subtract the mean and take the absolute value:

\[
|21 - 26| = | -5 | = 5
\]
\[
|25 - 26| = | -1 | = 1
\]
\[
|25 - 26| = | -1 | = 1
\]
\[
|26 - 26| = | 0 | = 0
\]
\[
|26 - 26| = | 0 | = 0
\]
\[
|27 - 26| = | 1 | = 1
\]
\[
|28 - 26| = | 2 | = 2
\]
\[
|30 - 26| = | 4 | = 4
\]

3. **List the absolute deviations:**

The absolute deviations are:

\[
\{5, 1, 1, 0, 0, 1, 2, 4\}
\]

4. **Calculate the mean of the absolute deviations:**

Now, calculate the sum of the absolute deviations:

\[
5 + 1 + 1 + 0 + 0 + 1 + 2 + 4 = 14
\]

Now, divide this sum by the number of data points to find the mean absolute deviation:

\[
\text{MAD} = \frac{14}{8} = 1.75
\]

Thus, the mean absolute deviation of the dataset is:

\[
\boxed{1.75}
\]