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}, follow these steps:

1. **Calculate the Mean**:
\[
\text{Mean} = \frac{\text{sum of the dataset}}{\text{number of values}}
\]

Sum of the dataset:
\[
23 + 24 + 26 + 27 + 28 + 30 + 31 = 189
\]

Number of values:
\[
7
\]

Thus, the mean is:
\[
\text{Mean} = \frac{189}{7} = 27
\]

2. **Calculate the Deviations from the Mean**:
Now find the absolute deviation from the mean for each value:
- |23 - 27| = 4
- |24 - 27| = 3
- |26 - 27| = 1
- |27 - 27| = 0
- |28 - 27| = 1
- |30 - 27| = 3
- |31 - 27| = 4

The absolute deviations are: {4, 3, 1, 0, 1, 3, 4}

3. **Calculate the Average Deviation**:
Average deviation is calculated as the mean of the absolute deviations:
\[
\text{Average Deviation} = \frac{\text{sum of absolute deviations}}{\text{number of values}}
\]

Sum of the absolute deviations:
\[
4 + 3 + 1 + 0 + 1 + 3 + 4 = 16
\]

Thus, the average deviation is:
\[
\text{Average Deviation} = \frac{16}{7} \approx 2.285714
\]

4. **Round to Nearest Hundredth**:
Rounding 2.285714 to the nearest hundredth gives:
\[
2.29
\]

The average deviation from the mean is **2.29**.