Uniform Distribution Calculator

<-- Enter a
<-- Enter b
<-- Enter x
<-- Optional Enter t if you are running the Moment Calculator

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

ƒ(680) = 0.01

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 = 333

Calculate the standard deviation σ
σ = √σ2
σ = √333
σ = 28.