This simulator gives you a ten-value dataset on a ruler and lets you drag one observation away from the rest. The mean balance point, the sorted middle pair that defines the median, and the squared-deviation columns behind variance all update live, so you can see exactly why they respond so differently to an extreme value.
• A real-time 3D scene with 4 inspectable parts (Data ruler and observations, Mean balance point, Sorted middle pair and Squared deviations), with home view, focus-selected-part, auto-rotate, expand, instrument-cover and hide-labels scene tools, plus a model response curve beneath the scene. • Experiment controls: Tenth observation (2-60); Spread of first nine observations (0.5-2); Repeatable random seed (1-99); show animated explanatory markers; pause/resume, 0.1 s and 1 s single-step buttons, four playback speeds and a restart button. • A Curves & measurements tab with a parameter-comparison chart, a live-measurements chart, the model equations and snapshot readouts (Mean; Median; Population variance; Sample variance; Sum of deviations from mean). • An Experiments tab with 2 guided presets (move the outlier and compact center) and a Model verification bench that runs independent fresh models, plus a timestamped event log and a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset and a written model-scope statement linking to a technical reference.
The mean is the balance point of the data, so one far-away value pulls it strongly. The median for ten values is the average of the fifth and sixth sorted observations, so it depends only on the middle of the ordering and barely moves when the tenth value becomes extreme. Variance sums squared deviations from the mean, so a single outlier contributes a very large column and inflates the spread.
The lab reports both population variance, which divides by n, and sample variance, which divides by n-1, along with the sum of deviations from the mean, which is always zero - a quick check that the balance point really is the mean.
The tenth-observation slider moves one value between 2 and 60 while a second slider sets the spread of the other nine, and a seed keeps the dataset repeatable. The animated balance markers are explanatory rather than a mechanical force solver.
Variance is expressed in squared data units, which is why the columns are drawn as squares, and the two variance formulas answer different questions: describing the dataset in hand versus estimating the variance of a wider population. The model uses a deterministic ten-value dataset, so it teaches concepts rather than analyzing your own data.
The median. It depends only on the sorted central positions, so moving the largest observation far away barely changes it, whereas the mean shifts toward the outlier. The outlier experiment in the simulator shows the two readouts diverging.
Squaring stops positive and negative deviations from cancelling - deviations from the mean always sum to zero - and it gives large deviations more weight. The result is in squared units, which the simulator draws as squares.
Population variance divides the sum of squared deviations by n and describes the dataset itself; sample variance divides by n-1 and is used to estimate the variance of a larger population from a sample. Both are shown so you can compare them.
No. With outliers or skewed data the median can describe a typical value better, and neither statistic alone describes spread. That is why the lab shows center and variance together.