Averages from Charts / Tables – AS Maths Revision – Statistics (S1)

The Easy Bit

  • If you don’t know how to find the mode from a table / chart / graph, go back to school
  • I’ll give you a clue – the mode is the outcome that occurs the most
  • This, of course, assumes there is a mode – there might not be one
  • If the data is grouped into classes, you can only find the modal class

Mean from a Frequency Table

  • Frequency tables give you the outcome in one column, and how many times it occurred (the frequency) in another column
  • You multiply each outcome by the number of times it occurred, and add those answers together… then you divide by the total frequency
  • It might help to make a new column to hold the outcome * frequency values before you add them together
  • Sometimes the outcomes are grouped into classes… in fact this is what you usually get in the exam
  • You can’t work out the exact mean from grouped data, because you don’t know the individual values – the result will be an estimate
  • The trick is to use the mid-point of each class in the same formula as before
  • …and that formula is… “x bar equals sigma fx over sigma f”
  • Don’t try to do this for qualitative data. It has to be numbers!

Median (or quartiles) from a Frequency Table or Stem and Leaf Diagram

  • The median will be the (n/2)th bit of data
  • This method also works for the quartiles: the (n/4)th and (3n/4)th bits of data
  • I’m not sure whether you round up your n/2 to the next integer, or go half way to the next one, or what – I never did quite get that – it’s something to do with whether it’s discrete or continuous data you’re dealing with
  • Anyway… if it’s a stem and leaf diagram, just count that number of items through, and you should land on your desired value
  • To get a median out of a frequency table, you’ll need to add a cumulative frequency column
  • (Cumulative frequency is the running total of the frequencies)
  • This will enable you to work out which outcome is the median (or whichever quartile you’re after)

Median (or quartiles) from a Grouped Frequency Table

  • When the frequency table is grouped into classes (and it pretty much always is), things get a little more complicated…
  • A little more complicated? You have to learn a formula!
  • You can use n/something, and the cumulative frequency column, as before, but instead of landing you right on the value you want, it’ll only tell you which class said value is in
  • To get an estimate of what the value is, you have to do linear interpolation
  • Basically, you’re assuming that the values in the class are all spread out evenly (and not bunched up in places)
  • I won’t try to explain how it works, in case I confuse myself! I just use the formula, and get the right answers (usually…)
  • The formula isn’t given to you in the exam, though…
  • Once again, I can’t draw the formula out for you, because this is a blog post – I shall now explain it

Interpolerpolerpolerpolerpolerpolationation (Interpolation)

  • You’ve worked out what class the median (or desired quartile) is in
  • You’ve also worked out the number of the value you’re looking for (n/2, n/4 or 3n/4, remember?)
  • Here’s what you do:
  • Subtract the total frequencies of all the classes below the one you’re looking in (the cumulative frequency column comes in handy, here) from the number of the value you’re looking for
  • Divide this by the frequency of the class you’re looking in
  • Multiply by the class width of the class you’re looking in
  • Add the lower boundary of the class you’re looking in
  • I hope that works. I’m rubbish at interpolation. (You have been warned).
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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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