This java applet is designed to display a simple boxplot (no outlier analysis), the Five-Number Summary (minimum, first quartile, median, third quartile, and maximum), the number of measurements (n), the mean, and the standard deviation for a collection of data. A toggle switch allows the student to view the corresponding histogram for the data along with the minimum, median, maximum, n, mean and standard deviation.
In the histogram window, the cell (bin) width is indicated and can be adjusted. Also, users are able to place the mouse cursor over an endpoint of the interval to display its value, and to click on a rectangle to display the percentage of data values that are in the corresponding interval. By changing the bin width, students are able to explore the effect bin width has on the shape and other characteristics of the histogram
Five data sets are provided or the student can enter her/his own data (A "load data from file" feature is available in the CD-ROM version of the National Library of Virtual Manipulatives).
By adding (deleting) data values, students are able to explore the effect individual values have on the boxplot and/or the histogram, the Five-Number Summary, the mean, and the standard deviation.
This website also includes instructions, teachers/parent notes and links to NCTM standards.
This material will help students to learn
1. How to make and interpret simple boxplots.
2. How to interpret histograms.
3. What the five number summary is.
4. The impact of cell width on the interpretation of a histogram.
5. That boxplots do not do a good job of representing bimodal data.
Target Student Population:
Appropriate for high school (and possibly middle school) students and introductory statistics students in college.
Prerequisite Knowledge or Skills:
Students should be familiar with how to calculate and interpret the Five-Number Summary, the mean, and the standard deviation.
Type of Material:
Either through a classroom demonstration or individual work, the effects of data manipulation on summary measures, the boxplot and the histogram can be illustrated. Also, the effects of bin width on characteristics of a histogram can be explored.
Evaluation and Observation
Interactive nature of the material would allow this to be a great demo in class. The overall clarity of presentation of the graphs, the easy to read numerical summaries, the ability to adjust cell widths would enable a lecturer to generate a lot of discussion with the few well chosen data sets.
The calculation of standard deviation is based on a divisor of n when determining the variance. This is not a problem, but should at least be pointed out.
It is not clear what rule the software is using to determine quartiles. It is not the usual rule used in K-12 statistics, which excludes the median from both the lower and upper "halves" when n is odd.
In the boxplot window, the mean appears to be marked in red below the boxplot, and an interval about the mean is displayed in green. A description of the interval is not provided and the meaning of the interval is not clear.The interval appears to be: Mean +/- (.5)(Standard Deviation).
Potential Effectiveness as a Teaching Tool
Data provided illustrate strengths and weakness of histograms and boxplots. Additional points can be added or given points deleted to see the changes which occur in the plots and the numerical summaries.
It would be useful to examine the effect of unusual data points on the range (if added) and the IQR (if added) and compare these with their effect on the standard deviation. Also, it would be useful if both the boxplot and histogram could be shown in the same window for an easier comparison. Finally, the teacher information might provide more guidance in how to connect the numerical summaries and the graphical representations.
Ease of Use for Both Students and Faculty
Very easy to learn to use, intuitive and obvious. The instructions provided will be helpful for those who may not be familiar with interactive web sites or who may miss some of the possible mouse overs. (Note: the instructions are entitled "Boxplots" but contain instructions for the histograms, too.) Connections are shown to the Math Standards will be useful in a pre-service teacher class.
When you clear the data using the clear button the information is lost immediately. This can be problematic if the user has entered a large number of values and accidentially hits clear.