Question

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

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 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

Therefore, the absolute deviations are: {4, 3, 1, 0, 1, 3, 4}.

3. **Calculate the Average Deviation**:
\[
\text{Average Deviation} = \frac{4 + 3 + 1 + 0 + 1 + 3 + 4}{7} = \frac{16}{7} \approx 2.2857
\]

4. **Round to the Nearest Hundredth**:
\[
\text{Average Deviation} \approx 2.29
\]

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