Find the average deviation of the given data set - 3,9,5,6,7

To find the average deviation (also called the mean absolute deviation) of a data set, follow these steps:

### Step 1: Find the Mean of the Data Set
First, calculate the mean (average) of the data points.

Given data set: \( 3, 9, 5, 6, 7 \)

\[
\text{Mean} = \frac{3 + 9 + 5 + 6 + 7}{5} = \frac{30}{5} = 6
\]

### Step 2: Calculate the Absolute Deviations
Next, subtract the mean from each data point and take the absolute value (ignoring negative signs).

\[
|3 - 6| = 3, \quad |9 - 6| = 3, \quad |5 - 6| = 1, \quad |6 - 6| = 0, \quad |7 - 6| = 1
\]

### Step 3: Find the Average of the Absolute Deviations
Finally, calculate the mean (average) of these absolute deviations.

\[
\text{Average Deviation} = \frac{3 + 3 + 1 + 0 + 1}{5} = \frac{8}{5} = 1.6
\]

### Conclusion:
The average deviation of the data set is \( 1.6 \).

Would you like more details or have any questions?

### 5 Related Questions:
1. How does average deviation differ from standard deviation?
2. What is the variance of this data set?
3. How do you calculate the median absolute deviation (MAD)?
4. What are the advantages of using average deviation over other dispersion measures?
5. Can we apply average deviation to grouped data sets?

### Tip:
For small data sets, average deviation is often a simpler way to measure variability compared to standard deviation.

Learn how to calculate the average deviation of the data set 3, 9, 5, 6, 7 with a step-by-step explanation. This solution covers key statistical concepts, including mean, absolute deviation, and average deviation, making it suitable for students in Grades 6-8.

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