Mean Deviation Calculator
Calculate mean absolute deviation (average deviation) from mean, median, or mode. Measure the dispersion of data points in a dataset.
Mean Deviation Result
Central Tendency
Data Summary
Step-by-Step Solution
Enter data and click "Calculate" to see the step-by-step solution.
Mean Deviation Formula
Mean Deviation = Σ|x - μ| / n
Where:
- Σ|x - μ| = sum of absolute deviations
- μ = mean/median/mode (central tendency)
- n = number of data points
Understanding Mean Deviation
- Measures average distance from center
- Lower value = data clustered near center
- Higher value = data spread out
- Always non-negative
- Less sensitive to outliers than standard deviation
When to Use
- Comparing variability of datasets
- Quality control in manufacturing
- Financial risk assessment
- Academic performance analysis
- Weather data analysis
Frequently Asked Questions
What is mean deviation?
Mean deviation (also called average deviation or mean absolute deviation) measures the average distance between each data point and the center of the dataset (mean, median, or mode). It shows how spread out the data is.
How do you calculate mean deviation?
Step 1: Find the mean (or median/mode) of the dataset
Step 2: Calculate the absolute difference between each data point and the center
Step 3: Sum all absolute differences
Step 4: Divide by the number of data points
What's the difference between mean deviation and standard deviation?
Mean deviation uses absolute values (|x - μ|), while standard deviation uses squared differences (x - μ)². Standard deviation gives more weight to outliers, while mean deviation treats all deviations equally. Standard deviation is more commonly used in statistical analysis.
Can mean deviation be negative?
No, mean deviation is always zero or positive because we use absolute values. A mean deviation of zero means all data points are identical (no spread).
What is a good mean deviation value?
A "good" mean deviation depends on your data. For test scores with a mean of 75, a mean deviation of 5 means most scores are within 5 points of 75 (clustered). A mean deviation of 15 means scores are more spread out.