Histograms – AS Maths Revision – Statistics (S1)

The x-axis…

  • Histograms represent grouped, continuous data (which is why the bars have no gaps between them)
  • It’s the area of the bar that represents the frequency, not the height of the bar
  • The edges of the bars are plotted at the class boundaries, so different bars usually have different widths
  • On the x-axis, you plot the continuous variable
  • On the y-axis, you plot either the frequency density, or the relative frequency density
  • If you know that a bar for a class of a certain class width is a certain number of centimetres wide on someone’s histogram, you can quite easily work out the class width of another class, given its width in centimetres on the histogram, or work out the width of its bar on the histogram, in centimetres, given its class width – just work out how much a single centimetre represents

That y-axis…

  • Frequency density is frequency divided by class width
  • Relative frequency is frequency divided by total frequency
  • For this reason, the area isn’t always equal to the frequency (as it was at GCSE)
  • The area is proportional to the frequency…
  • The constant of this proportionality is the same for each bar, though, so you can work out frequencies and areas
  • The examiners like to give you questions where you have to work out the dimensions of a bar given its frequency, or the frequency given its dimensions,¬†with a known bar to compare it with. Using the known bar, work out the constant linking the area to the frequency. You can work out the width / class width as described above. Height = Area / Width, but you already knew that
  • I have no idea how to get means, modes and medians from a histogram. Convert it back into a group frequency table, I suppose. In the event that we’re asked to do that, common sense should hopefully prevail
  • Ooh, the modal class is probably the one with the biggest area on the histogram!

About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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