How to Solve Mean Deviation Problems
Solve mean deviation aptitude problems step by step, with a worked example and practice questions with answers.
Expected Interview Answer
Mean deviation measures the average absolute distance of every data point from a central value (usually the mean), computed as MD = Σ|xi − x̄| / n, and it quantifies spread in the same units as the original data.
The calculation has three steps: find the central value (typically the mean), compute the absolute difference of every point from that center, then average those absolute differences. Taking the absolute value is essential — without it, positive and negative deviations from the mean would always cancel to exactly zero, since the mean is defined as the balance point of the data. Mean deviation is simpler to compute than variance or standard deviation because it skips squaring, but it is used less often in advanced statistics because absolute value functions are harder to work with algebraically than squares. A larger mean deviation signals more spread-out data; a mean deviation near zero signals values clustered tightly around the center.
- Directly interpretable in the same units as the data
- Simple three-step process: center, absolute difference, average
- A quick, intuitive way to compare spread across two datasets
AI Mentor Explanation
A batter’s scores across five innings average 40 runs; the mean deviation is the average of how far each individual innings score sits from that 40-run mean, ignoring whether the innings was above or below it. A player who scores consistently near 40 every match has a small mean deviation, while a player who alternates between ducks and centuries has a large one even with the same average. Taking the absolute distance is crucial — without it, the too-high and too-low innings would simply cancel out to zero.
Worked example
Mean
- (4+6+8+10+12)/5
- = 8
Absolute deviations
- 4, 2, 0, 2, 4
Mean deviation
- Sum = 12
- 12/5 = 2.4
Step-by-Step Explanation
Step 1
Compute the central value
Usually the mean: x̄ = Σxi / n.
Step 2
Find absolute deviations
Compute |xi − x̄| for every data point.
Step 3
Sum the absolute deviations
Add all the |xi − x̄| values together.
Step 4
Divide by n
MD = Σ|xi − x̄| / n gives the mean deviation.
What Interviewer Expects
- Correct computation of the mean before deviations
- Understanding why absolute value is required, not signed deviation
- Correct final division by n
- Interpreting a larger mean deviation as more spread
Common Mistakes
- Forgetting to take absolute value, so deviations cancel to zero
- Dividing by n−1 instead of n (confusing with sample variance conventions)
- Using the wrong central value (median instead of mean when mean is asked)
- Arithmetic slips when summing several deviations
Best Answer (HR Friendly)
“Mean deviation is the average distance every value sits from the center, always measured as a positive distance regardless of direction. You find the mean first, take the absolute difference of each point from it, then average those absolute differences. It is a simple way to describe how spread out data is, in the same units as the original numbers.”
Follow-up Questions
- How does mean deviation differ from standard deviation in what it measures?
- Why do statisticians use squared deviations more often than absolute deviations?
- How would mean deviation about the median differ from mean deviation about the mean?
- How does an extreme outlier affect the mean deviation compared to the standard deviation?
MCQ Practice
1. Dataset: 2, 4, 6, 8, 10. What is the mean deviation about the mean?
Mean = 6. Absolute deviations: 4,2,0,2,4, sum=12, MD = 12/5 = 2.4.
2. Why must absolute value be used when computing mean deviation from the mean?
The mean is the balance point of the data, so signed deviations always sum to exactly zero without absolute value.
3. A dataset has mean deviation 0. What must be true?
Zero mean deviation means every value is exactly at the center, so all values must be identical.
Flash Cards
Mean deviation formula? — MD = Σ|xi − x̄| / n.
Why absolute value, not signed difference? — Signed deviations from the mean always sum to zero, canceling out any spread information.
What does a larger MD indicate? — More spread — data points sit farther from the center on average.
How many steps to compute MD? — Three: find the mean, take absolute deviations, average them.