What's the difference between descriptive and inferential statistics?

Descriptive statistics summarize and describe data (mean, median, standard deviation), while inferential statistics make predictions or inferences about a population based on a sample (hypothesis testing, confidence intervals).

When should I use a Z-test vs T-test?

Use a Z-test when you know the population standard deviation and have a large sample size (n > 30). Use a T-test when you don't know the population standard deviation or have a small sample size. T-tests are more common in practice.

What does R-squared tell us in regression analysis?

R-squared measures the proportion of variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, with higher values indicating a better fit. However, a high R-squared doesn't necessarily imply causation.

Statistics Calculator

Calculate descriptive statistics, analyze probability distributions, perform hypothesis testing, and conduct regression analysis. Learn statistical concepts with comprehensive explanations and real-time calculations.

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Comprehensive Statistics Calculator for All Your Analytical Needs

Descriptive Statistics

Calculate mean, median, mode, standard deviation, variance, and more

Probability Distributions

Normal, binomial, and Poisson distributions with detailed analysis

Hypothesis Testing

Z-tests, T-tests with p-values and confidence intervals

Regression Analysis

Linear regression with R², correlation, and prediction capabilities

Statistical Formulas & Real-World Applications

Essential Formulas

Mean: μ = Σx / n

Variance: σ² = Σ(x - μ)² / n

Standard Deviation: σ = √σ²

Z-Score: z = (x - μ) / σ

Correlation: r = Σ((x - μₓ)(y - μᵧ)) / (nσₓσᵧ)

Regression Slope: b = r(σᵧ / σₓ)

Practical Applications

Quality Control: Monitor manufacturing processes using control charts

Market Research: Analyze survey data and customer preferences

Healthcare: Clinical trial analysis and treatment effectiveness

Finance: Risk assessment and investment analysis

Education: Test score analysis and educational research

Sports Analytics: Player performance and team statistics

Statistical Analysis Tips:

Check for Normality: Many statistical tests assume normal distribution. Sample Size Matters: Larger samples provide more reliable results. Understand P-Values: p < 0.05 suggests statistical significance. Correlation ≠ Causation: Just because two variables are related doesn`‘t mean one causes the other.

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