▭ Uniform Distribution Calculator
Calculate density and cumulative probability for a continuous uniform distribution.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate density and cumulative probability for a continuous uniform distribution.
| Concept | Formula or rule |
|---|---|
| Uniform Distribution Calculator | f(x)=1/(b−a) · F(x)=(x−a)/(b−a) for a≤x≤b |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: For Uniform(0,10), every interval of equal length has equal probability.
✓ P(X≤6)=0.6 and density=0.1
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Treating density as point probability
For a continuous variable, P(X=x)=0.
For a continuous variable, P(X=x)=0.
⚠️
Using b≤a
The upper bound must exceed the lower bound.
The upper bound must exceed the lower bound.
⚠️
Assuming all real data are uniform
Uniformity is a modeling assumption.
Uniformity is a modeling assumption.
Practice Questions
1. Uniform(0,4): what is density?
Answer: 0.25
2. Uniform(2,8): what is mean?
Answer: 5
3. Uniform(0,10): P(X≤3)?
Answer: 0.3
Frequently Asked Questions
What is the mean?▾
(a+b)/2.
What is the variance?▾
(b−a)²/12.
Is density constant?▾
Yes within the interval.