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**:

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

Sum of the data:

\[
23 + 24 + 26 + 27 + 28 + 30 + 31 = 189
\]

Number of data points:

\[
7
\]

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

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

Next, we find the absolute deviations from the mean (27):

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

The absolute deviations are: 4, 3, 1, 0, 1, 3, 4.

3. **Calculate the average of these absolute deviations**:

Sum of absolute deviations:

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

Now, we divide by the number of data points:

\[
\text{Average Deviation} = \frac{16}{7} \approx 2.285714285714286
\]

Rounding to the nearest hundredth:

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

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