April 2025
Intermediate to advanced
324 pages
6h 56m
English
Content preview from Think Stats, 3rd Edition
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Chapter 4. Cumulative Distribution Functions
Frequency tables and PMFs are the most familiar ways to represent distributions, but as we’ll see in this chapter, they have limitations. An alternative is the cumulative distribution function (CDF), which is useful for computing percentiles, and especially useful for comparing distributions.
Also in this chapter, we’ll compute percentile-based statistics to quantify the location, spread, and skewness of a distribution.
Percentiles and Percentile Ranks
If you have taken a standardized test, you probably got your results in the form of a raw score and a percentile rank. In this context, the percentile rank is the percentage of people who got the same score as you or lower. So if you are “in the 90th percentile,” you did as well as or better than 90% of the people who took the exam.
To understand percentiles and percentile ranks, let’s consider an example based on running speeds. Some years ago I ran the James Joyce Ramble, which is a 10 kilometer road race in Massachusetts. After the race, I downloaded the results to see how my time compared to other runners.
Instructions for downloading the data are in the notebook for this chapter. The relay.py module provides a function that reads the results and returns a Pandas DataFrame:
fromrelayimportread_resultsresults=read_results()results.head()
| Place | Div/Tot | Division | Guntime | Nettime | Min/Mile | MPH | |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1/362 | M2039 | 30:43 | 30:42 | 4:57 | 12.121212 |
| 1 | 2 | 2/362 | M2039 | 31:36 | 31:36 | 5:06 ... |
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