Mean vs Median vs Mode: Measures of Central Tendency
Three averages, three different stories about your data. The CA Foundation Statistics section tests when each measure is appropriate and how to calculate them.
head-to-Head Comparison
| Basis | Mean (Arithmetic Mean) | Median |
|---|---|---|
| Definition | Sum of all values divided by the number of values (x̄ = Σx/n) | The middle value when data is arranged in order; divides distribution into two halves |
| Effect of Extreme Values | Highly affected by outliers (a very high/low value pulls the mean) | Not affected by extreme values (positional average) |
| Algebraic Treatment | Can be treated algebraically (e.g., combined mean of groups) | Cannot be treated algebraically |
| Data Type Suitability | Best for symmetric distributions with no extreme outliers | Best for skewed distributions (e.g., income data) |
| Relationship (Skewed Data) | In positively skewed data: Mean > Median > Mode | In positively skewed data: Median lies between Mean and Mode |
The 'Karl Pearson's Empirical Formula' Trap
Karl Pearson's empirical relationship: Mode = 3 × Median − 2 × Mean. This formula is used to estimate Mode when it is ill-defined (e.g., in continuous data). Don't confuse this with the strict definition of Mode. Also note: this is an empirical (approximate) formula, not exact.
Common Ground (Similarities)
- Both are Measures of Central Tendency that summarize a data set with a single representative value.
- Both are used in the calculation of other statistical measures (e.g., Mean Deviation).
- For a perfectly symmetrical distribution, Mean = Median = Mode.
Test Your Understanding
Q1: In a perfectly symmetrical distribution, which of the following is correct?
Mean > Median > Mode
Mean < Median < Mode
Mean = Median = Mode ✅
Mode = 3 Median − 2 Mean
Explanation: In a perfectly symmetrical (bell-shaped/normal) distribution, all three measures of central tendency coincide at the center.
Q2: Which measure of central tendency is NOT affected by extreme values?
Mean
Geometric Mean
Median ✅
Weighted Mean
Explanation: Median is a positional average determined by the middle observation(s) in ordered data. Extreme values at either end don't change the middle position.