๐ Foundational Thought
Card: Measures of Spread
How we understand variation, dispersion, and the shape of
difference in data
1. Background Context
- After
identifying the center of a dataset (via mean, median, or mode), we
must ask:
How far do values stray from that center?
- Measures
of spread (also called dispersion) tell us how consistent,
volatile, or unequal the data is.
A center alone is misleading without knowing how far things
vary around it.
2. Core Concept
Measures of spread describe the extent to which data
points differ from each other or from a central value.
They tell us whether a dataset is tight or wide, predictable or scattered.
3. Foreground Measures
|
Measure |
Description |
Best Use |
|
๐ Range |
Max – Min |
Simple sense of span (but sensitive to outliers) |
|
๐งฎ Variance (ฯ²) |
Average squared distance from the mean |
Theoretical foundation for many models |
|
๐ Standard Deviation
(ฯ) |
Square root of variance; in same units as data |
Most common measure of spread |
|
๐ฐ Interquartile
Range (IQR) |
Difference between 75th and 25th percentiles |
Robust to outliers; shows middle spread |
|
๐งฎ MAD (Mean Absolute
Deviation) |
Average of absolute deviations from the mean |
Simpler and more intuitive than variance in some contexts |
4. Current Relevance
- Finance:
Standard deviation measures investment volatility
- Education:
Test scores with same mean but different spread = different learning
outcomes
- Social
Science: Income spread tells more about inequality than averages alone
- Healthcare:
Variation in patient response crucial for treatment evaluation
Spread often reveals what averages hide.
5. Visual / Metaphoric Forms
- Range
is the “stretch” of the data rubber band
- Standard
deviation is the “typical wobble” around the center
- IQR
is the “heart of the hive”—where the central 50% lives
6. Real-World Example: Income Inequality
|
Dataset A |
Dataset B |
|
Mean: $50,000 |
Mean: $50,000 |
|
Std Dev: $5,000 |
Std Dev: $50,000 |
Both have the same average—but in Dataset B, wealth is
concentrated in a few hands.
Spread tells the truth behind the average.
7. Blind Spot Warnings
- Outliers
skew range and variance
- Standard
deviation assumes normality—not always valid for skewed data
- IQR
omits extreme values—great for robustness, but hides tails
- No
one measure tells the whole story
8. Reflective Prompts
- What
does the spread of my data suggest about reliability or fairness?
- Am I
too focused on the center—missing important variation?
- How
do different kinds of spread change my interpretation?
9. Fractal & Thematic Links
- ๐
Central Tendency – center is meaningless without understanding
variation
- ๐
Skewness & Kurtosis – describe shape of spread
- ๐
Uncertainty & Risk – all modeled using spread
- ๐ง
Cognitive Bias – humans often ignore variance and assume averages
Use This Card To:
- Evaluate
consistency, inequality, or volatility in a dataset
- Add
nuance to interpretation beyond central tendency
- Communicate
why one average is not like another
- Design
fairer systems or policies informed by range, not just center