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 will follow these steps:

1. **Calculate the mean** of the dataset.
2. **Calculate the absolute deviations** from the mean.
3. **Calculate the average of these absolute deviations**.

### Step 1: Calculate the Mean

\[
\text{Mean} = \frac{\text{Sum of the data}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{23 + 24 + 26 + 27 + 28 + 30 + 31}{7}
\]
\[
\text{Mean} = \frac{189}{7} = 27
\]

### Step 2: Calculate the Absolute Deviations from the Mean

Next, we'll calculate the absolute difference of each data point 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

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

### Step 3: Calculate the Average of the Absolute Deviations

\[
\text{Average Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of data points}}
\]
\[
\text{Sum of absolute deviations} = 4 + 3 + 1 + 0 + 1 + 3 + 4 = 16
\]
\[
\text{Average Deviation} = \frac{16}{7} \approx 2.28571428571
\]

### Final Step: Round to the Nearest Hundredth

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

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