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Recently I was doing histograms in mathematics. My teacher told me to label the y axis as frequency density but often some graphs only have frequency. So what is the difference between frequency density and just frequency graphs?

Secondly what is the difference between histograms and bar graphs. My teacher said that discrete data is represented on a bar graph and continuous data on a histogram. However I found a photo that showed a histogram displaying test marks from 0 - 30. This data doesn't seem continuous. So what really is the difference?

James Chadwick
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  • Please only ask one question per post. – Jam Oct 17 '22 at 07:55
  • Does this answer your question? What is the Difference between Frequency and Density in a Histogram? – Jam Oct 17 '22 at 07:56
  • Re. your second question, in a nutshell, histograms take numerical independent variables while bar charts take categorical IVs. So histograms' "bars" must be read in horizontal order, while that isn't a strict stipulation for bar charts. While you would tend to plot continuous IVs with a histogram, you could very well do so for discrete IVs, you just incur a limit on how granular the bunched up sub-intervals can be. (Even in the case of continuous IVs, you're grouping them up, so it's functionally like a discrete variable.) – Jam Oct 17 '22 at 08:04
  • @Jam Thanks for your answer. Could you briefly simply what "You just incur a limit on how granular the bunched up sub-intervals can be." means? It's the only part I can't quite understand. – James Chadwick Oct 17 '22 at 08:12
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    @user1098338 If have a continuous IV, say ranging over the interval from $0$ up to $30$, you would be able to divide that into sub-intervals whichever way you wanted, e.g. as $[0, 0.9), [0.9, 27.3), [27.3, 30]$. If you have a discrete IV, the data would have a "resolution", in a sense, restricting how it can be divided up. For example, if the IV takes integer values, you could have $[0, 1], [2, 27], [28, 30]$, but your sub-intervals must lie on the integers. That sense of chunkiness or resolution is what I mean by "granularity". But in either case, you can make a histogram. – Jam Oct 17 '22 at 08:37
  • @Jam So we can essentially graph discrete data on a histogram if it acts continuous? – James Chadwick Oct 17 '22 at 08:46
  • @user1098338 I wouldn't phrase it as "acts continuous", but essentially yes, all we want is for the data to be numerical (i.e. continuous or discrete). What is necessary is that we can put the IVs in order on an $x$-axis. (NB: some texts do want the IV to be exclusively continuous for a true histogram, so check which definition you are using first.) – Jam Oct 17 '22 at 08:55
  • @Jam Ahh so the parameters of a histogram is slightly ambiguous? – James Chadwick Oct 17 '22 at 09:09

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