Expectation (Average)
Variance (Spread)
& Histogram
3 Statistical Moments
- Expected Value ($\mathbb{E}[X]$): Represents the weighted average or center of mass of the distribution. It predicts the long-run average outcome of random experiments. $$\mathbb{E}[X] = \sum x_i \cdot p(x_i)$$
- Variance ($\text{Var}(X)$): Quantifies the spread or dispersion of the data points around the mean. A high variance indicates that data points are spread far from the mean. $$\text{Var}(X) = \sum (x_i - \mathbb{E}[X])^2 \cdot p(x_i)$$
INTERACTIVE Distribution & Statistics
Lock Total (100%)
Explore Mean ($\mathbb{E}[X]$) and Variance ($\text{Var}(X)$) interactively. Drag the dots to change values, or use sliders to adjust probability weights.
Mean $\mathbb{E}[X]$
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Variance $\sigma^2$
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Std Dev $\sigma$
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Probability Weights
VISUALIZER Understanding Histograms
A histogram estimates the probability distribution of a continuous variable. Adjust bins to see how it affects the shape.
Bins:
20
Controls Granularity
500