Showing 12 results
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.
El Niño Southern Oscillation (ENSO)
Visualize the Pacific Ocean trade winds, thermocline shift, and upwelling mechanisms that govern El Niño and La Niña climate phases.
Retinal Disparity & Binocular Cues
Simulate how the left and right eyes receive slightly different 2D images, allowing the brain to compute 3D depth and convergence angles.
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.
Maxwell-Boltzmann Distribution
Visualize how temperature and molar mass shift the kinetic energy distribution of particles, affecting the proportion that overcome the Activation Energy.
The Calvin Cycle
Track the fixation of Carbon Dioxide by Rubisco and the energy transfer from Light-Dependent ATP/NADPH to synthesize G3P.
Chain Rule Visualizations
Mechanical gear visualization translating the abstract composite derivative multiplication f'(g(x)) * g'(x) into physical rotational interlocking.