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📚 Online Statistics Education
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1 Introduction2 Graphing Distributions3 Summarizing Distributions4 Describing Bivariate Data5 Probability6 Research Design7 Normal Distribution8 Advanced Graphs9 Sampling Distributions10 Estimation11 Logic of Hypothesis Testing12 Tests of Means13 Power14 Regression15 Analysis of Variance16 Transformations17 Chi Square18 Distribution Free Tests19 Effect Size
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3.4 Balance Scale Simulation

This section is an interactive demonstration. The live simulation runs on the original site: open the demonstration at onlinestatbook.com.

Learning Objectives

  1. Understand what it means for a distribution to balance on a fulcrum
  2. Learn which measure of central tendency will balance a distribution.

Instructions
This demonstration allows you to see the point at which the distribution balances for different shaped distributions.

The graph in the right panel is a histogram of 600 scores. The mean and median are equal to 8 and are indicated by small vertical bars on the X axis The top portion of the bar is in blue and represents the mean. The bottom portion is in pink and represents the median. The mean and median are also shown to the left of the Y axis.

You can see that the histogram is balanced on the tip of the triangle (the fulcrum). The triangle beneath the X-axis is always at the point where the histogram is balanced. In these slides you will see differently shaped distributions. See if you can determine the relationship between the mean, median, and/or the mode and the location of the balance point.

Slide Show

Adapted from Online Statistics Education: A Multimedia Course of Study (onlinestatbook.com), Project Leader: David M. Lane, Rice University. Developed with NSF support. The original work is in the public domain; it is cited here at the authors' request. Changes were made: reformatted as an accessible XYZ web edition with native MathML. License: Public-Domain.