How this calculation works
If the bounds coincide, the only possible integer is certain and variance is zero.
THE FORMULA
Mean = (a+b)/2, variance = ((b−a+1)²−1)/12A worked example
The five integers 2 through 6 have mean 4 and variance 2.
Good to know
Every integer between the bounds has the same probability.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Summarize equally likely integers on an inclusive range.
The primary result is labeled “Mean”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Every integer between the bounds has the same probability.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
The five integers 2 through 6 have mean 4 and variance 2.
Which rule does this calculator apply?
Mean = (a+b)/2, variance = ((b−a+1)²−1)/12