Histograms

[Alexei Kassymov]

My understanding of histograms was that the counts are read based on the area (e.g. the total area of the bars equals the numbers of cases/observations; with percentages/proportions as counts, the areas add to 1). The example on page 6 (animal speeds) uses the height of the bars as counts. For example, there are 5 animals slower than 10 mi/h and the height of the bar is 5. If the method above is used, there should be 50 animals in the data slower than 10 mi/h.

Are CC histograms more like bar charts with bars placed next to each other?

[Bill McCallum]

You are right, this is a bar chart, not a histogram, the progression should be corrected here.

[Lisa j r]

I would like to see further discussion on this topic. While I do understand what Alexei is referring to I also believe that the example as presented in the progressions is how students are taught histograms in the early years. Can we get more input? If the example in the progressions is incorrect, are there further examples or resources that teachers could be directed to.

[Bill McCallum]

I really don’t think this is an important mathematical or pedagogical issue. Clearly there is some confusion about the meanings of the terms “histogram” and “bar chart.” While it would be a good idea for the field to come to some common understanding of the meanings of these terms, I do not think it’s an important concern for students of mathematics in these grades. In the end, we want them to be able to correctly read and produce these graphical representations of data. That’s the most important thing. What words they use for them is less important. Textbooks and teachers should be consistent in whatever terminology they use, of course.

[Cathy Kessel]

Alexei Kassymov seems to be talking about what Wikipedia calls “normalized histograms” and what the Guidelines for Assessment and Instruction in Statistics Education Report (GAISE) report calls “relative frequency histograms.”

In the Standards, as in the GAISE report (see p. 35), bar graphs are for categorical data with non-numerical categories, while histograms are for measurement data which have been grouped by intervals along the measurement scale.

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