Hassan Ijaz
Ai, Web & Design
Measures of central tendency and spread
Interactive dataset builder where users add/remove points and see mean, median, mode, and spread measures update with visual indicators
Concept Overview
Measures of central tendency and spread are fundamental descriptive statistics that summarize the main characteristics of a dataset. They help us understand where data is centered and how much it varies.
Measures of Central Tendency
Mean (Average)
- Sum of all values divided by count: x̄ = Σx/n
- Sensitive to outliers - can be pulled by extreme values
- Best for symmetric distributions without outliers
- Has nice mathematical properties (minimizes squared errors)
Median
- Middle value when data is sorted
- Robust to outliers - extreme values don't affect it
- Better for skewed distributions
- 50th percentile of the data
Mode
- Most frequently occurring value(s)
- Can have multiple modes (bimodal, multimodal)
- Only measure that works for categorical data
- May not exist or may not be unique
Measures of Spread (Dispersion)
Range
Maximum - Minimum
Simplest but most sensitive to outliers
Interquartile Range (IQR)
Q3 - Q1 (75th percentile - 25th percentile)
Contains middle 50% of data, robust to outliers
Variance & Standard Deviation
- Variance: Average squared deviation from mean
- Standard deviation: Square root of variance (σ)
- In same units as data (unlike variance)
- Forms basis for many statistical tests
Relationships Between Measures
Distribution shapes affect measure relationships:
- Symmetric: Mean ≈ Median ≈ Mode
- Right-skewed: Mode < Median < Mean
- Left-skewed: Mean < Median < Mode
Choosing the Right Measure
- Income data: Use median (skewed by high earners)
- Test scores: Use mean (usually symmetric)
- Categorical data: Use mode (only option)
- Data with outliers: Use median and IQR
Use the interactive tool below to add and remove data points. Watch how different measures of central tendency and spread update in real-time, and see visual indicators showing their positions on the distribution.
Interactive Visualization
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Interactive dataset builder where users add/remove points and see mean, median, mode, and spread measures update with visual indicators