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Quartiles divide sorted data into four equal parts. Q1 (25%), Q2 (50%/median), and Q3 (75%) mark the boundaries.
Formula
IQR = Q3 - Q1 (Interquartile Range)
The IQR contains the middle 50% of data. Outliers are typically defined as values below Q1-1.5×IQR or above Q3+1.5×IQR.
Quartiles require sorted data. Always arrange from smallest to largest.
When multiple values equal a quartile boundary, interpolation may be needed.
Box plots visually display the five-number summary and highlight outliers.
Quickly understand data spread and identify unusual values.
Compare individual scores to population distribution.
Economists use quartiles to study income distribution.
Sort data, find the median (Q2), then find medians of lower and upper halves (Q1 and Q3).
Min, Q1, Median, Q3, Max. It describes data distribution and creates box plots.
An outlier is typically outside [Q1 - 1.5×IQR, Q3 + 1.5×IQR].
Q1 = 25th percentile, Q2 = 50th, Q3 = 75th. Percentiles divide data into 100 parts.