This applet is designed to allow users to explore the relationship between histograms and the most typical summary statistics. The user can choose from several types of histograms (uniform, normal, symmetric, skewed, etc.), or can create their own by manipulating the bars of the histogram. The statistics available for display are mean, median, mode, range, standard deviation, and interquartile range. Also available is a "Practice Guessing" option, in which the values of the statistics are hidden until the user has entered guesses for each value.
Java. No special plug-ins required. Worked well in Firefox.
Content Quality Concerns:
The "normal" histogram is more of a triangle than a bell shape. All of the pre-made histograms are too perfect. For example, the uniform histograms have exactly the same height in each bar. I think this misses an opportunity to show the variability that you would see with real data. A different approach might be to include a random number generator and display the histogram of a random sample each time. Each bar of the histogram is a different color, which is not how histograms really look. Also, it would have been nice to show definitions of mean, median, mode, and the measures of spread. Is IQ the IQR? This IQ terminology isn't standard. I would like to see a link that you could click on to see an example of how the program calculates these summary statistics for a particular distribution.
Content Quality Strengths:
Colorful, simple approach to illustrating how measures of center and spread change as the distribution changes. It allows the user to see interaction between statistics and graphs quickly. Users can see and create many graphs. Another strength is in the choices of display symbols for the statistics. For example, the mean is a triangle, which reference how it "balances" the histogram. The standard deviation is displayed as a bar centered at the mean.
Ease of Use Concerns:
I would like to see a reminder on the applet pop-out window to click on a bar to manipulate the distribution. I didn't read the instructions carefully enough the first time (similar to what a student might do), and then I couldn't figure out what I was supposed to do other than clicking on the summary statistics boxes. I also didn't think to check the 'distribution' tab at the top until much later. I think the guessing game should have its own tab. I had trouble switching between modes'once I was done with the guessing game for one distribution, I had to go to the distribution tab to switch to another distribution before I could go back to the guessing game for a new distribution. If you shut down the applet window, you can't click on the link to start it back up again without leaving the website altogether. The button just says "Running" and won't let you do anything. This is acknowledged in the 'Bugs' section, but it would be nice if the problem could just be fixed. The directions are on the launch page, rather than on the applet. This means that some (like me at first) will miss the fact that you can change the bars of the histogram. Each bar in the histogram is a different color. This is not very attractive.
Ease of Use Strengths:
Colorful, inviting, easy to manipulate. The applet is very easy to use. Most choices are made using intuitive clicks and drags of the mouse.
Potential Effectiveness Concerns:
Without well-designed questions to accompany the applet, I am concerned that students will just click buttons without thinking about what they are seeing. The "skewed left" and "skewed right" histograms happen to have the same mean and median, which I believe will tend to mislead students in the relationship between the two statistics. It would be helpful if the student had access to some sample calculations to explain how the computer gets the values for the summary statistics.
Potential Effectiveness Strengths:
The students can definitely see the relationship between statistics. For example, the bar for standard deviation is centered at the mean, the range is insensitive to the majority of the data points, etc. It is easy to think of questions that could be asked based on this module. (Why is IQ always < range? Try to create a histogram that makes the mean and median as different as possible. Try to create two histograms where the range stays the same, but the standard deviation changes. And so on.)
Potential Effectiveness Rating:
Source Code Available:
Source Code Available
Intended User Role:
Free for All