Five Number Summary
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The Interquartile Range (IQR = Q3 − Q1) represents the middle 50% of your data. It's a robust measure of spread that isn't affected by outliers, unlike standard deviation. A large IQR indicates high variability; a small IQR indicates the data is tightly clustered around the median.

Sort the data in ascending order. Q1 is the median of the lower half (all values below the median). Q3 is the median of the upper half (all values above the median). If the dataset has an even number of values, the median is the average of the two middle values — this median value is excluded when calculating Q1 and Q3.

A box plot (box-and-whisker plot) visually displays the five number summary. The box spans from Q1 to Q3 (the IQR), with a line at the median. Whiskers extend to the minimum and maximum (or to the outlier fences). Points beyond the whiskers are plotted individually as outliers.

Use the five number summary when your data is skewed, has outliers, or is not normally distributed — it's robust because the median and quartiles are not distorted by extreme values. Use mean and standard deviation when data is approximately normally distributed and you need to work with parametric statistics. For example, income data is best described by the five number summary (heavily right-skewed), while height data works well with mean ± SD.

For an odd number of values: the median is the exact middle value. Q1 is the median of all values below the middle; Q3 is the median of all values above the middle (the middle value itself is excluded from both halves). For an even number: the median is the average of the two middle values. Q1 is the median of the lower half; Q3 is the median of the upper half. Different statistical software may use slightly different conventions (there are multiple valid methods).

If the median line is closer to Q1 than Q3, the data is right-skewed (positively skewed) — most values cluster low with a long tail of high values. If the median is closer to Q3, the data is left-skewed. If the box is asymmetric with a very long upper whisker, there are extreme high values. Symmetric box plots with a centered median suggest normally distributed data. Box plot shape guides which statistical tests are appropriate.