Showing 12 results
Sampling Distributions (CLT)
Struggle with the Central Limit Theorem? Draw 10,000 samples from highly skewed or bimodal parent populations and watch the perfect normal bell curve emerge.
Residual Plots
Evaluate the appropriateness of Least Squares Regression Lines (LSRL). Detect curvilinear patterns, heteroscedasticity, and influential outliers.
Binomial Distribution
Model discrete probability distributions for fixed trials with $P(X=k) = inom{n}{k}p^k(1-p)^{n-k}$. Visualize how the number of trials and success probability affect the shape, mean $mu = np$, and standard deviation $sigma = sqrt{np(1-p)}$ of binomial distributions.
Boxplot & Outlier Visualizer
Visualize five-number summaries (minimum, Q1, median, Q3, maximum) in boxplots and identify outliers using the IQR rule. Explore how outliers beyond $Q1 - 1.5 imes IQR$ or $Q3 + 1.5 imes IQR$ affect data distribution and summary statistics.
Central Limit Theorem
Visualize how sampling distributions of means approach normality as sample size increases, regardless of population shape. Explore the CLT formula $sigma_{ar{x}} = rac{sigma}{sqrt{n}}$ and see how larger samples produce tighter distributions around the population mean.
Confidence Intervals
Construct confidence intervals using $ar{x} pm z^* rac{sigma}{sqrt{n}}$ to estimate population parameters. Visualize how confidence level, sample size, and variability affect interval width, and interpret what it means to be 95% confident about capturing the true parameter.
Hypothesis Testing
Conduct hypothesis tests by calculating test statistics and p-values to evaluate null hypotheses. Visualize Type I and Type II errors, significance levels, and the decision-making process for rejecting or failing to reject the null hypothesis based on sample evidence.
Least Squares Regression Line
Calculate the least squares regression line $hat{y} = a + bx$ that minimizes the sum of squared residuals. Visualize how the slope $b = r rac{s_y}{s_x}$ and intercept relate to correlation, and interpret the line's predictive power for bivariate data.
Scatter Plot & Correlation
Create scatter plots to visualize bivariate relationships and calculate correlation coefficient $r$ to measure linear association strength. Explore how outliers, direction, form, and strength affect correlation, and understand why correlation does not imply causation.
Least Squares Regression Predictor
Dynamically adjust a line of best fit to actively minimize the sum of squared residuals (SSE) compared to the true OLS regression model.
Margin of Error Simulator
Visualize exactly what the Margin of Error means geometrically. Observe how increasing sample size shrinks it while demanding higher confidence widens it.
Normal Distribution Explorer
Interactive Gaussian curve generator manipulating $\mu$ and $\sigma$ instantly mapped against the 68-95-99.7 Empirical Rule. Highlights discrete $Z$-score thresholds tracking precision standard deviation geometry exactly.