Normal and Lognormal Distributions: Mode, Median, and Mean

① This example dynamically illustrates the density curves of the normal and lognormal distributions, highlighting the positions of the mode, median, and mean on each curve to reveal how these central tendency measures differ between symmetric and skewed distributions. ② Core mathematical concepts include probability density functions, distribution parameters (mean μ, standard deviation σ), skewness, and the relationships among mode, median, and mean in symmetric versus skewed data. ③ Construction details: Based on the construction summary, sliders (e.g., μl, σl, μn, σn) control distribution parameters, function graphs plot the density curves, and point objects (i, g, k, h, j, p) mark the mode, median, and mean. Additional elements like surfaces or parabolas may support visualization, but the core relies on function graphing and slider interactivity. ④ Suitable for high school to undergraduate statistics courses, as well as introductory data analysis, helping learners intuitively compare characteristic values and understand how skewness affects measures of central tendency.