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 (give a solid number)

Answer 1

To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, follow these steps:

1. **Calculate the mean**:
\[
\text{Mean} = \frac{23 + 24 + 26 + 27 + 28 + 30 + 31}{7} = \frac{189}{7} = 27
\]

2. **Calculate the 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. **Calculate the sum of the absolute deviations**:
\[
4 + 3 + 1 + 0 + 1 + 3 + 4 = 16
\]

4. **Calculate the average deviation**:
\[
\text{Average Deviation} = \frac{16}{7} \approx 2.285714285714286
\]

5. **Round to the nearest hundredth**:
\[
\text{Average Deviation} \approx 2.29
\]

Thus, the average deviation from the mean is **2.29**.