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The definition of a histogram is a graph in which the x-axis is a quantitative variable split into bins, and the y-axis is the frequency. However, if we want to graph some other property of the bins (not the frequency), is the resulting graph still a histogram? Or is it considered a bar graph?

For example, say the x-axis is the age of the residents of a city, split into bins of size 10 years. We graph the total income of the residents in each bin. (The y-axis is income.) Is the resulting graph a histogram or a bar graph or something else? (I read that the bar graph is supposed to have categorical, not quantitative, variables on the x-axis.)

carbenoid
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  • When you plot averages it's a [regressogram](http://stats.stackexchange.com/questions/51840/rationale-for-the-use-of-regressogram-bin-smooth); in your case (where it's total rather than average) you might call it a graph of binned total income by age – Glen_b Sep 15 '16 at 21:55
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    This appears to be a nonstandard definition of "histogram." The usual definition is that histograms use *areas* (not lengths or heights) to represent frequencies or densities. ([Google](https://www.google.com/search?q=histogram+definition) and [Wikipedia](https://en.wikipedia.org/wiki/Histogram#Mathematical_definition) are clear about that. Also see our threads on histograms, such as http://stats.stackexchange.com/questions/24568, where the distinction is particularly important.) Your definition describes a bar graph of frequency. – whuber Sep 15 '16 at 21:56

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