Login
📚 Online Statistics Education
Chapters ▾
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
⇩ Download ▾
⇩ This section (Typst)

7.4 Varieties Demonstration

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

Learning Objectives

  1. State the relationship between the mean and standard deviation of a distribution and its shape.
  2. Be able to describe differences in distributions based on their shape and statistics.

Instructions
This demonstration allows you to change the mean and standard deviation of two normal distributions and observe the effects on the shapes of the distributions.When the demonstration begins, the red distribution has a mean of 50 and a standard deviaton of 10. The blue distribution has a mean of 50 and a standard deviation of 5. Notice how much more spread out the red distribution is than the blue distribution.

Choose different values for the two distributions and investigate their effects.

Illustrated Instructions
The demonstration starts by displaying two curves both with a mean of 50 and with standard deviations of 10 and 5 respectively. You can change the values for the mean and standard deviation for both curves.
Screenshot of the normal-distribution demonstration comparing two curves with the SAME mean and different spreads: the red curve has Mean 50, Sd 10 and the blue has Mean 50, Sd 5. Both peak at 50 on an axis from 0 to 100, but the blue curve is roughly twice as tall and half as wide, since both enclose the same area.

The screenshot below shows the distributions with different means and standard deviations. Note that the curves are on an axis that ranges from 0 - 100, keep this in mind when changing the values of the mean and standard deviations as some values will not be displayed correctly.
Screenshot of the same demonstration after changing the parameters so the curves differ in both respects: red has Mean 70, Sd 10 and blue has Mean 50, Sd 15. The blue curve is centered further left and is lower and broader; the red is centered at 70 and is taller and narrower. The two overlap substantially between about 40 and 90.

We recommend you answer the questions even if you have to guess. Then use the simulation to help you if necessary.

You can change the the means and standard deviations of both distributions by typing values in the respective fields below.

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.