📊 Measures of Central
Tendency
How we find the “center” of data—and what that center
really means
1. Background Context
- In
statistics, when we observe a collection of data points, we often want to
ask:
“What’s typical?” or “Where does the data tend to gather?”
- Measures
of central tendency answer that by giving us a single value that
represents the center or average of the dataset.
2. Core Concept
Measures of central tendency are summary numbers that
describe the “middle” or “typical” value in a dataset.
The three main types are:
- Mean
– arithmetic average
- Median
– middle value
- Mode
– most frequent value
Each tells a different story depending on the shape
and nature of the data.
3. Foreground Comparison
|
Measure |
Description |
Best Used When |
Example |
|
📈 Mean |
Sum of all values ÷ number of values |
Data is symmetric and free of outliers |
Average test score |
|
📍 Median |
Middle value when data is sorted |
Data is skewed or has outliers |
Household income |
|
🔁 Mode |
Most frequently occurring value |
Categorical or discrete data |
Most common shoe size |
4. Current Relevance
- Policy:
Median income used to assess economic well-being
- Medicine:
Mean blood pressure vs. median recovery time
- Education:
Mean test scores used to evaluate performance
- Data
Science: Choice of central tendency affects model accuracy and insight
quality
Different measures are appropriate in different contexts.
Using the wrong one can mislead.
5. Visual / Metaphoric Forms
- Mean
is the balance point – like a see-saw’s fulcrum
- Median
is the median strip – the middle of the road
- Mode
is the crowd’s favorite – the value most people pick
6. Blind Spot Warnings
- Mean
is sensitive to outliers: A few extreme values can distort the average
E.g., one billionaire can skew the “average income” in a
small town
- Median
ignores extremes: Good for fairness, but loses information about tails
- Mode
can be multiple or unclear: In uniform or continuous distributions,
the mode may not be useful
7. Reflective Prompts
- What
kind of “center” am I really trying to understand?
- Am I
using the right measure for the shape of my data?
- What
happens if I report only one measure—what do I miss?
8. Fractal & Thematic Links
- 📐
Distribution Shape – skewness affects choice of center
- 📊
Outliers – can distort or mask the story the data tells
- 🔍
Data Summary – central tendency + spread = real insight
- 🧠
Cognitive Bias – our minds often assume “average” = “normal” (not
always true)
Use This Card To:
- Choose
the appropriate summary statistic in data analysis
- Teach
or communicate the nuance behind “averages”
- Guard
against simplification in social or policy discussions
- Reflect
on how the “center” is defined—and who it serves