Question

A group of friends compared the number of houseplants each person owned. The dataset they recorded is {1, 1, 3, 5, 8}

What is the average deviation from the mean number of houseplants?

(1 point)
Write your answer rounded to the nearest hundredths if necessary.

The average deviation from the mean is

Answer 1

To find the average deviation from the mean, follow these steps:

1. **Calculate the mean** of the dataset.
2. **Calculate the absolute deviations** from the mean for each data point.
3. **Calculate the average of those absolute deviations**.

### Step 1: Calculate the Mean

The dataset is {1, 1, 3, 5, 8}.

\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{1 + 1 + 3 + 5 + 8}{5} = \frac{18}{5} = 3.6 \]

### Step 2: Calculate the Absolute Deviations

Now, calculate the absolute deviation from the mean for each value:

- For 1: \( |1 - 3.6| = 2.6 \)
- For 1: \( |1 - 3.6| = 2.6 \)
- For 3: \( |3 - 3.6| = 0.6 \)
- For 5: \( |5 - 3.6| = 1.4 \)
- For 8: \( |8 - 3.6| = 4.4 \)

The absolute deviations are: \( 2.6, 2.6, 0.6, 1.4, 4.4 \).

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

Now, sum the absolute deviations and divide by the number of values:

\[ \text{Sum of absolute deviations} = 2.6 + 2.6 + 0.6 + 1.4 + 4.4 = 11.6 \]

\[ \text{Average deviation} = \frac{11.6}{5} = 2.32 \]

Thus, the average deviation from the mean is **2.32**.