Uniform Distribution Calculator

Publish date: 2024-07-18

Given a uniform distribution with a = 670, b = 770, and x = 680, Calculate the probability density function ƒ(680), μ, and σ2

The uniform distribution probability is denoted below for a < x < b:

ƒ(x) =	1
	b - a

Plugging in our values for a, b, and x, we get:

ƒ(680) =	1
	770 - 670

ƒ(680) =	1
	100

Calculate the mean μ

μ =	a + b
	2

μ =	670 + 770
	2

μ =	1440
	2

μ = 720

Calculate the median:

The median equals the mean → 720

Calculate the variance σ2:

σ2 =	(b - a)2
	12

σ2 =	(770 - 670)2
	12

σ2 =	1002
	12

σ2 =	10000
	12

σ2 = 833.33333333333

Calculate the standard deviation σ

σ = √σ2
σ = √833.33333333333

σ = 28.867513459481

What is the Answer?

σ = 28.867513459481

How does the Uniform Distribution Calculator work?

Free Uniform Distribution Calculator - This calculates the following items for a uniform distribution
* Probability Density Function (PDF) ƒ(x)
* Cumulative Distribution Function (CDF) F(x)
* Mean, Variance, and Standard Deviation
Calculates moment number t using the moment generating function
This calculator has 4 inputs.

What 2 formulas are used for the Uniform Distribution Calculator?

μ = ½(a +b)
ƒ(x) = 1 / (b - a)

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Uniform Distribution Calculator?

meanA statistical measurement also known as the averagemomenta function are quantitative measures related to the shape of the functions graphstandard deviationa measure of the amount of variation or dispersion of a set of values. The square root of varianceuniform distributionStatistical distribution with constant probability
M = 1/(b - a)varianceHow far a set of random numbers are spead out from the mean

Example calculations for the Uniform Distribution Calculator