Question

What is the mean absolute
deviation of the following
dataset: 4.8, 5.9, 6.2, 10.8,
1.2, 6.4? Express your answer
as a decimal rounded to the
nearest tenth.

Answer 1

To calculate the Mean Absolute Deviation (MAD) of the dataset \( 4.8, 5.9, 6.2, 10.8, 1.2, 6.4 \), we will follow these steps:

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

\[
\text{Mean} = \frac{\sum \text{data points}}{n} = \frac{4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4}{6}
\]

First, we calculate the sum:

\[
4.8 + 5.9 + 6.2 + 10.8 + 1.2 + 6.4 = 35.3
\]

Now, divide by the number of data points (which is 6):

\[
\text{Mean} = \frac{35.3}{6} \approx 5.8833
\]

2. **Calculate the absolute deviations from the mean for each data point.**

\[
|4.8 - 5.8833| \approx 1.0833
\]
\[
|5.9 - 5.8833| \approx 0.0167
\]
\[
|6.2 - 5.8833| \approx 0.3167
\]
\[
|10.8 - 5.8833| \approx 4.9167
\]
\[
|1.2 - 5.8833| \approx 4.6833
\]
\[
|6.4 - 5.8833| \approx 0.5167
\]

3. **Sum the absolute deviations.**

\[
1.0833 + 0.0167 + 0.3167 + 4.9167 + 4.6833 + 0.5167 = 11.5167
\]

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

\[
\text{MAD} = \frac{\text{Sum of Absolute Deviations}}{n} = \frac{11.5167}{6} \approx 1.91945
\]

5. **Round the result to the nearest tenth.**

The mean absolute deviation, rounded to the nearest tenth, is:

\[
\text{MAD} \approx 1.9
\]

Thus, the mean absolute deviation of the dataset is **1.9**.