Variance & Standard Deviation
Quartiles divide a sorted dataset into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 is the overall median, Q3 (75th percentile) is the median of the upper half. The IQR (Q3−Q1) measures the middle 50% spread.
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Pro Tip
For odd numbers of data points: exclude the median when calculating Q1 and Q3. For even: include all data in each half. Different methods exist — statistical software may calculate quartiles slightly differently.
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Did You Know?
Box-and-whisker plots (box plots), invented by John Tukey in 1970, show quartiles visually. They are particularly useful for comparing distributions across groups and quickly spotting outliers and skew.
References
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