🎲 Median

Median#

The middle value separating the higher and lower halves of data.

Important

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What it is#

The median is the middle value of the data once sorted — for an odd count the single center value, for an even count the average of the two middle values. It splits the data into two equal halves and is exactly the 0.5 quantile.

Its strength#

The median is robust to outliers — extreme values change which point sits in the middle only slightly, and never by their magnitude, so its breakdown point is 50%. That resilience makes it the right summary for skewed data (income, house prices) and the value that minimizes absolute error.

The trade-off#

The median ignores the magnitudes of all but the central values, so it discards information the mean uses, and it is harder to manipulate algebraically. It needs orderable data — it works on ordinal, not nominal, values.

Theme: Probability & Statistics Foundations · All terminology

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Mind map — connected ideas

Mean · Outlier · Quantile Level · Normal Distribution · Regression Models · Mean Squared Error (MSE)

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