‘Coding’ and Measures of Dispersion – AS Maths Revision – Statistics (S1)

Ranges

  • Measures of dispersion are numerical methods of representing the spread of data
  • The range is the range (biggest value minus smallest value)
  • In all the past papers I’ve done, I’ve never seen a question with anything at all to do with the range
  • They do quite like the inter-quartile range, though – it’s useful for finding outliers
  • It’s the upper quartile minus the lower quartile
  • I never did introduce you to the quartiles. They’re like the median, except 25% through and 75% through, rather than 50% through (that’s all there is to it)

Standard Deviation

  • Standard Deviation wasn’t on my GCSE Maths syllabus, and I didn’t do GCSE Statistics, so I’d never encountered it before
  • That’s why it’s got a lot of bullet points here
  • I’ve noticed the formula for it is a bit hard to remember, and isn’t in the formula booklet…
  • It’s gonna be really difficult for me to explain… but here goes
  • The standard deviation is the square root of the variance
  • The variance is… “sigma x squared f, over sigma f… minus the mean squared”
  • So you’ll need a new column for the outcome (or mid-point of the class, if you’re estimating) squared, multiplied by the frequency
  • You then total that column and divide by the total frequency
  • After that, subtract the mean, and square root the whole thing
  • I hope I’m right about that!

No, it’s not programming

  • Coding is when data sets are simplified so that things can be worked out more easily
  • Surprisingly, it doesn’t mess up finding these things
  • I’m putting it here, because there’s not much to say about it, so it can’t have its own post!
  • Data¬†are coded according to a formula given in the question (although I suppose it’s a possibility that you might be asked to work out what the coding formula is…)
  • Once you’ve worked out your coded result, you may need to undo the coding to get the actual result
  • Some things have to be uncoded (decoded?), whereas other things aren’t affected

Undoing the Coding

  • The Correlation Coefficient, r (Pearson’s Product Moment one) is not affected by coding – you don’t need to do anything to your result
  • The mean can be uncoded by substituting it back into the coding formula
  • Coded regression lines can be uncoded by substituting the coding formulae into the regression line equation, then simplifying until it’s back in regression line format
  • The standard deviation is uncoded differently depending on what coding you used – if the coding is just adding or subtracting something from each bit of data, the spread is unaffected, however, if the coding includes multiplying, you may have to un-multiply
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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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