Probability & Statistics Calculator
A probability & statistics calculator simplifies complex mathematical operations for data analysis. It helps users calculate measures like mean, median, mode, standard deviation, probability distributions (binomial, normal), and confidence intervals. Essential for students, researchers, and professionals, it streamlines statistical hypothesis testing, data interpretation, and predictive modeling, enabling informed decision-making in fields like finance, engineering, and social sciences.
Formulas Used
Probability: P(A) = favorable outcomes / total outcomes
Mean: μ = Σx/n
Median: Middle value of sorted data
Standard Deviation: σ = √(Σ(x-μ)²/n)
Binomial Probability: P(k) = C(n,k)p^k(1-p)^(n-k)
Normal Distribution: Z = (X-μ)/σ
How to Use
1. Select calculation type from dropdown
2. Enter numerical data (comma-separated)
3. For probability calculations, enter parameters like success/failure counts
4. Click Calculate to get instant results
5. Use Clear button to reset inputs
Results show both numerical answers and methodological explanations for verification.
Derivation Process
This calculator combines fundamental statistical formulas developed through mathematical theory and empirical research. Probability calculations stem from classical combinatorics, while statistical measures derive from descriptive statistics principles established by pioneers like Gauss and Pearson. Algorithms were implemented using JavaScript's math functions, with input validation ensuring data integrity. The system was tested against known datasets to verify accuracy.