A percentile is a value below which a specified percentage of an ordered dataset falls. It turns a long list of numbers into an interpretable position: the 50th percentile is the median, while the 25th and 75th percentiles mark the first and third quartiles. section 2.15 section 2.12
Use percentiles to read both typical values and the spread of the middle half:
- The 25th percentile leaves about 25% of observations below it; the 75th leaves about 75% below it. section 2.15
- Subtracting the 25th percentile from the 75th gives the interquartile range, which summarizes the middle 50% while reducing the effect of outliers. section 2.15
- A quantile expresses the same idea using a fraction rather than a percentage: quantile = percentile/100. section 2.15
Reading a set of bar tabs
For bar tabs [7, 18, 19, 20, 21, 22, 25, 120, 1500], NumPy gives the 25th, 50th, and 75th percentiles as 19, 21, and 25. Thus, the middle 50% lies between 19 and 25, producing an interquartile range of 6 despite the unusually large tabs. section 2.15
import numpy as np bar_tabs = [7, 18, 19, 20, 21, 22, 25, 120, 1500] q25 = np.percentile(bar_tabs, 25) q50 = np.percentile(bar_tabs, 50) q75 = np.percentile(bar_tabs, 75) # 19.0 21.0 25.0 print(q25, q50, q75)
Run the NumPy example to calculate the 25th, 50th, and 75th percentiles. section 2.15
