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Uniform distribution of mantissas

As explained in Statistics Every Programmer Needs

The uniform distribution of mantissas is the property that logarithmic fractional parts are uniformly distributed between zero and one.

The uniform distribution of mantissas states that the fractional parts of logarithmic data fall uniformly between 0 and 1 when the data follows Benford’s law. section 12.1

Use the property as an additional check on logarithmic patterns:

  • Compute the logarithmic fractional parts rather than relying only on leading-digit frequencies. section 12.1
  • Judge conformity from the overall mantissa distribution; mean and variance provide supporting insight but are not sufficient alone. section 12.1

Logarithmic fractional parts

The values log10(2) ≈ 0.301 and log10(1.1111111) ≈ 0.046 illustrate mantissa values within the 0–1 interval. section 12.1

How Statistics Every Programmer Needs covers it

How deep it goes
Defines the property and recommends examining the overall distribution, while deferring detailed mantissa statistics.
Examples
Uses log10(2) ≈ 0.301 and log10(1.1111111) ≈ 0.046 as mantissa examples.
What it assumes
Assumes familiarity with logarithms and Benford’s law while defining mantissa uniformity directly.
What you can do after
Evaluate Benford conformity by comparing the observed mantissa distribution with uniformity from 0 to 1.
How it connects
Connects logarithmic scale, fractional parts, leading digits, and Benford’s law.
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This explainer was generated by Manning's knowledge graph from the text of Statistics Every Programmer Needs. The section links point to the parts of the book it draws on.