Distribution Shapes Anchor Chart
Statistics & Data Analysis Guide
Mean Median Mode
Shapes of Data Distributions
How data clusters, where tails stretch, and how outliers pull the Mean away from the center.
The Golden Rule: "The tail tells the tale!" The skew direction is always named after the longer tail, never the peak.
Mean follows the tail
Negative Skew Skew < 0
Left-Skewed
Long tail extends to the left
Mode Median Mean Long Tail Left
Order of Central Tendency
Mean < Median < Mode
▪ Tail: Stretches to the left
▪ Peak: Concentrated on the right
▪ Pull: Low outliers pull Mean down
Real Example:
Easy exam scores or age at death (most survive to older ages; rare early deaths stretch tail left).
Zero Skew Skew ≈ 0
Symmetrical
Bell-shaped; balanced tails
All In Center Balanced / Mirror Image
Order of Central Tendency
Mean = Median = Mode
▪ Tail: Equal length on both sides
▪ Peak: Directly in the center
▪ Pull: Balanced; no pull in either direction
Real Example:
Adult heights, standardized test scores (SAT/IQ), and shoe sizes in a homogenous population.
Positive Skew Skew > 0
Right-Skewed
Long tail extends to the right
Mode Median Mean Long Tail Right
Order of Central Tendency
Mode < Median < Mean
▪ Tail: Stretches to the right
▪ Peak: Concentrated on the left
▪ Pull: High outliers pull Mean up
Real Example:
Household income or home prices (most earn modest income; super-rich pull tail far to the right).
Quick Comparison Matrix
Essential Exam Reference
| Distribution | Tail Direction | Peak Position | Inequality Relation | Best Center Measure |
|---|
| Left-Skewed (Negative) | Points Left (←) | Right side | Mean < Median < Mode | Median (Resistant) |
| Symmetrical (Normal) | Balanced / Both sides | Center | Mean = Median = Mode | Mean or Median |
| Right-Skewed (Positive) | Points Right (→) | Left side | Mode < Median < Mean | Median (Resistant) |
Why does the Mean shift?
The Mean calculates total sum, making it highly sensitive to extreme outliers in the tail. The Median only counts positional order, resisting skew.
Toes Memory Trick
Look down at your feet: your left foot slopes down to the left (Left-Skewed); your right foot slopes down to the right (Right-Skewed)!
