Lesson 2 of 8 · All lessons in this module
- Mean, median, mode and outliers
- Quantiles, box plots and their uses
- Range, mean absolute deviation, variance and standard deviation
- Target downside deviation and coefficient of variationVideo lesson
- Skewness and kurtosisVideo lesson
- Scatter plots, covariance and correlation
- Limits of correlation analysis
- Integrated cases: describing one return series from raw data
Lesson 2 of 8 · 14 min
Quantiles, box plots and their uses
Quantiles mark the values at or below which a given share of the sorted data lies, so they show where any observation stands relative to the rest.
In short
- Quartiles split sorted data into 4 equal parts, quintiles into 5, deciles into 10 and percentiles into 100. The median is Q2, the 5th decile and the 50th percentile.
- In raw data the y-th percentile sits at position ; interpolate when the position is not a whole number.
- The interquartile range IQR = Q3 − Q1 covers the middle 50% of the data and ignores extremes.
- A box-and-whisker plot draws the IQR as a box with the median inside, and whiskers out to the extremes or to fences 1.5 × IQR beyond the box.
- Investors use quantiles to rank managers against peers and to sort stocks into groups, such as size deciles, for research.
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