Question

Calculate the average deviation from the mean for the following dataset: {23,24,26,27,28,30,31} . Round your answer to the nearest hundredth.(1 point)
The average deviation from the mean is

Answer 1

To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, we first need to find the mean of the dataset.

1. **Calculate the mean:**

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

\[
\text{Sum} = 23 + 24 + 26 + 27 + 28 + 30 + 31 = 189
\]

\[
\text{Number of values} = 7
\]

\[
\text{Mean} = \frac{189}{7} = 27
\]

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

\[
|23 - 27| = 4
\]
\[
|24 - 27| = 3
\]
\[
|26 - 27| = 1
\]
\[
|27 - 27| = 0
\]
\[
|28 - 27| = 1
\]
\[
|30 - 27| = 3
\]
\[
|31 - 27| = 4
\]

3. **Sum of absolute deviations:**

\[
4 + 3 + 1 + 0 + 1 + 3 + 4 = 16
\]

4. **Calculate the average deviation:**

\[
\text{Average Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of values}} = \frac{16}{7} \approx 2.285714286
\]

5. **Round the answer to the nearest hundredth:**

\[
\text{Average Deviation} \approx 2.29
\]

Therefore, the average deviation from the mean is \( \boxed{2.29} \).