Statistics for Beginners in Excel – Uniform Distribution

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(Basic Statistics for Citizen Data Scientist)

Uniform Distribution

When you ask for a random set of say 100 numbers between 1 and 10, you are looking for a sample from a continuous uniform distribution, where α = 1 and β = 10 according to the following definition.

Definition 1: The continuous uniform distribution has probability density function (pdf) given by

Uniform distribution pdf

where α and β are any parameters with α < β.

Observation: The corresponding cumulative distribution function (cdf) is

Uniform distribution function

The inverse cumulative distribution function is

I(p) = α + p(β − α)

Other key statistical properties are:

  • Mean = (α + β) / 2
  • Median = (α + β) / 2
  • Mode = any xα ≤ x ≤ β
  • Range = (-∞, ∞)
  • Variance = (β – α)2 / 12
  • Skewness = 0
  • Kurtosis = -1.2


Real Statistics Functions: Excel doesn’t provide any functions for the uniform distribution. Instead you can use the following functions provided by the Real Statistics Resource Pack.

UNIFORM_DIST(x, α, β, cum) = the pdf of the continuous uniform distribution f(x) at x when cum = FALSE and the corresponding cumulative distribution function F(x) when cum = TRUE.

UNIFORM_INV(p, α, β) = x such that UNIFORM_DIST(x, α, β, TRUE) = p. Thus UNIFORM_INV is the inverse of the cumulative distribution version of UNIFORM_DIST.


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Statistics for Beginners in Excel – Uniform Distribution


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