5 random data points give 94% median certainty with no assumptions
A simple trick from 'How to Measure Anything' lets you estimate the median with tiny samples.
Deep Dive
A method from Douglas Hubbard's book shows that with just 5 random independent samples, you can be approximately 94% confident the population median lies between the sample minimum and maximum. The probability is 1 - (1/2)^(n-1). No knowledge of the underlying distribution is needed—only that it has a median. The main tradeoff: the approach is likely extremely sensitive to outliers (the sample max and min are maximally sensitive, and combining them could be even more so), but it offers a quick, assumption-free estimate.
Key Points
- With n=5 random samples, probability that median is between min and max = 93.75%
- Formula: confidence = 1 - (1/2)^(n-1); works for any distribution with a median
- Extreme outlier sensitivity is main drawback; no assumptions needed
Why It Matters
Small-sample estimation without distribution assumptions empowers data-poor decisions with rigorous confidence bounds.