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Central Limit Theorem Lab

Math · Central Limit Theorem Lab · Middle School and High School

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关于这个模拟实验

Draw repeated samples from uniform, skewed or two-peaked populations. Compare the population histogram with the histogram of sample means.

学生可以探索什么

Predict how increasing sample size changes the spread and shape of sample means.

学习目标

1Predict how increasing sample size changes the spread and shape of sample means.

教师常问的问题

What assumptions does this simulation use?

Independent samples from bounded finite-variance populations. The normal overlay is a large-sample approximation; small samples retain population shape.

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继续探索

Spin a spinner, flip a coin or roll a die and watch two sets of bars: the chances the shapes predict, and the results you actually got. Ten spins prove nothing; a few hundred and the two are hard to tell apart.

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Type any function and see its shape straight away. Plot up to three at once in three colours to compare them, drag the trace point to read a value off a curve, and see where each one crosses zero.

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Move m and watch the line tilt; move b and watch it slide. Or drag the two points on the line and read the equation it writes back. A rise-over-run staircase climbs the line so slope becomes something you can count.

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Two bodies under gravity trace an ellipse forever and you can write the formula down. Add a third and no such formula exists. Run the figure-eight orbit, nudge one mass, and watch a stable pattern become unpredictable while the total energy stays put.

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Riemann Sums and the Integral Simulation的预览图

Approximate the area under a curve with strips and choose how each takes its height: left edge, right edge, middle, or a sloping top. Push the strip count up and watch the error fall, with the running total plotted as its own curve.

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从模型到记录

学生探索之后，用工作表记录他们的预测、观察和解释。