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Calculate percentiles, quartiles, IQR, and percentile rank with box plot visualization, step-by-step solutions, and Python code.
Separate numbers with commas, spaces, or new lines
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Quick Reference:
Quartiles are specific percentiles that divide data into four equal parts. Q1 = 25th percentile, Q2 = 50th percentile (median), Q3 = 75th percentile. Percentiles provide finer granularity with 100 divisions.
By default, numpy.percentile() uses linear interpolation. It computes the rank as (p/100)*(n-1), then linearly interpolates between the two nearest data points. You can change this with the method parameter (e.g., "lower", "higher", "nearest", "midpoint").
Use IQR when your data has outliers or is skewed. IQR only considers the middle 50% of data, making it robust to extremes. Standard deviation uses all data points and is heavily influenced by outliers. For normally distributed data, both are appropriate.
Calculate Q1, Q3, and IQR = Q3 - Q1. Any value below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is considered a mild outlier. Values beyond Q1 - 3*IQR or Q3 + 3*IQR are extreme outliers. This is known as Tukey's fence method.
The five-number summary consists of: minimum, Q1 (25th percentile), median (50th percentile), Q3 (75th percentile), and maximum. It provides a complete picture of data spread and is the basis for box plot visualizations.