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I have been working with some histograms(using frequency and not frequency density) and I noticed that sometimes people have the first interval longer than the rest of the intervals.

See below for example: Site here

The first interval of the frequency table is 10-0 = 10 units long, while the second is 20-11 = 9 units long. But the histogram is drawn as if the intervals are the same length. Isn't this a bit misleading-especially when using frequency instead of frequency density?

This also will make it confusing for understanding the interval given if we were to be presented with the histogram as we may think that the intervals are $0\leq x < 10$, $10\leq x < 20$, $20\leq x < 30$, but this is not the case as the first interval must be $0\leq x \leq 10$

Need help

I would like some advice on why this is ok to have the first interval longer than the rest as this surly will misrepresent the data.

enter image description here

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    $\begingroup$ Note that the data set is for a continuous variable. (Ostensibly, at least---I don't think anyone is getting paid 1/3 of a thousand dollars a year.) So those bins also wouldn't make sense in that they seemingly exclude [10,11], [20,21], etc. I'd assume them as just being sloppy in the labeling and the bins are actually (using interval notation) [0,10), [10,20), etc, but it's not possible to be sure without knowing how the histogram was constructed in the first place. $\endgroup$
    – Semiclassical
    Commented Jul 7 at 14:32

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I had a similar thought as expressed in Semiclassical's comment. The histogram intervals in the graph cover equal amounts of salary, but way the intervals are labeled in the table is wrong. The first interval $(\$0-\$10,000)$ is fine, but the second interval starts directly at $\$11,000$, which skips the entire salary amount from $\$10,001-\$10,999$. This happens to all the other intervals as well, which is definitely not right.

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