Find the average deviation of the mean 1,5,4,2

To calculate the **average deviation** (also known as **mean absolute deviation**) of the given set of numbers 1, 5, 4, and 2, follow these steps:

1. **Find the mean (average):**
   \[
   \text{Mean} = \frac{1 + 5 + 4 + 2}{4} = \frac{12}{4} = 3
   \]

2. **Calculate the absolute deviations from the mean:**  
   Subtract the mean from each number and take the absolute value:
   \[
   |1 - 3| = 2, \quad |5 - 3| = 2, \quad |4 - 3| = 1, \quad |2 - 3| = 1
   \]

3. **Find the average of these absolute deviations:**
   \[
   \text{Average Deviation} = \frac{2 + 2 + 1 + 1}{4} = \frac{6}{4} = 1.5
   \]

So, the **average deviation** of the mean is **1.5**.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How is standard deviation different from average deviation?
2. How do you calculate variance from a data set?
3. What is the median of this data set?
4. Can the average deviation be negative?
5. How would the average deviation change if a new number, say 6, is added to the data set?

**Tip:** The average deviation helps understand the dispersion of data points around the mean, while standard deviation offers a more refined view by squaring deviations.

Discover how to calculate the average deviation of the mean for the data set 1, 5, 4, and 2. This guide covers key statistical concepts like the mean and mean absolute deviation, with a detailed step-by-step solution. Suitable for students in Grades 6-8.

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