Module 1 · Descriptive Statistics · Topic 5
Quartiles. Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half. Q2 is the overall median (50th percentile). Q3 (75th percentile) is the median of the upper half.
Outlier Detection. A data point is a suspected outlier if it falls below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. These boundaries are called the lower and upper fences.
IQR = Q3 − Q1
xbar = sum(x_i) / n — The arithmetic average of a data set.s^2 = sum((x_i - xbar)^2) / (n - 1) — Average squared distance from the sample mean with Bessel correction.Data: {1, 3, 5, 7, 9, 11, 13}. Lower half: {1, 3, 5}, Q1 = 3. Upper half: {9, 11, 13}, Q3 = 11. IQR = 11 − 3 = 8. Lower fence = 3 − 12 = −9. Upper fence = 11 + 12 = 23. No outliers.
The five-number summary - minimum, Q1, median, Q3, maximum - gives a quick picture of the data’s center, spread, and range. It is the basis for box plots.
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