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Everyone including books and people answering on this website get this wrong. It does matter and the rule is simple. If your horizontal access is something where it is not possible to rank in any special order- for example favourite crisp flavours or different ways of getting to work - then the bars are separate. I think spacing of a third or half the bar width looks neatest.

If you have a horizontal axis of some grouped data, like length of leaves, then you have a histogram and the bars touch. Strictly a histogram has a vertical axis of density to accommodate different width groupings. In many cases all the widths are identical and you have a simple frequency up the vertical axis.

There does not seem any unaminity of the correct name for this animal. On the one hand I'd use "histogram" so it's clear the bars touch but then some purists object because the vertical axis isn't density. On balance I'd still call it a histogram.

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