Question

What is the mean absolute deviation of this data set?



3.4, 7.3, 2.5, 3.8, 7.5, 2.8

Answer 1

To find the mean absolute deviation (MAD) of the data set, follow these steps:

1. **Calculate the mean of the data set.**

The data set is:
\[ 3.4, 7.3, 2.5, 3.8, 7.5, 2.8 \]

Sum of the data set:
\[ 3.4 + 7.3 + 2.5 + 3.8 + 7.5 + 2.8 = 27.3 \]

Number of data points:
\[ n = 6 \]

Mean (\(\mu\)):
\[ \mu = \frac{27.3}{6} = 4.55 \]

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

For each data point, calculate the absolute deviation:
- For \(3.4\): \(|3.4 - 4.55| = 1.15\)
- For \(7.3\): \(|7.3 - 4.55| = 2.75\)
- For \(2.5\): \(|2.5 - 4.55| = 2.05\)
- For \(3.8\): \(|3.8 - 4.55| = 0.75\)
- For \(7.5\): \(|7.5 - 4.55| = 2.95\)
- For \(2.8\): \(|2.8 - 4.55| = 1.75\)

3. **List the absolute deviations:**
- \(1.15, 2.75, 2.05, 0.75, 2.95, 1.75\)

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

Sum of the absolute deviations:
\[ 1.15 + 2.75 + 2.05 + 0.75 + 2.95 + 1.75 = 11.4 \]

Mean absolute deviation (MAD):
\[ \text{MAD} = \frac{11.4}{6} \approx 1.9 \]

So, the mean absolute deviation of the data set is approximately **1.9**.