🎲 Mean

Mean#

The arithmetic average of a set of values.

Important

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What it is#

The (arithmetic) mean is the average — the sum of all values divided by their count:

\[\mu = \frac{1}{n}\sum_{i=1}^{n} x_i.\]

It uses every data point, which makes it the natural summary of a symmetric distribution and the value that minimizes squared error.

Its weakness#

Because it incorporates every value, the mean is sensitive to outliers and skew — a single extreme value drags it toward the tail. Statisticians say its breakdown point is 0%: one bad point can move it arbitrarily. On skewed data like income, the mean overstates where most values sit.

When to use it#

Prefer the mean for roughly symmetric, outlier-free numeric data, where it is efficient and mathematically convenient (it feeds variance, standard error, regression). For skewed or outlier-heavy data, reach for the median. It is undefined for categorical data.

Theme: Probability & Statistics Foundations · All terminology

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Mind map — connected ideas

Median · Outlier · Mean Squared Error (MSE) · Normal Distribution · Standard Error (SE) · Regression Models

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More in Probability & Statistics Foundations

Beta Distribution · Confidence Level · Correlation · Critical Value · Cumulative Distribution Function (CDF) · Frequentist · IID (Independent and Identically Distributed) · Likelihood · Margin of Error (MoE) · Median · Normal Distribution · Outlier · Population Proportion · Probability