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Measures of spread

Comparing results

  • Sometimes it is good to be able to compare results from different populations. For example compare a student's performance in two or more classes.
  • To do this, we can calculate the number of standard deviations a student is away from the mean.
  • For example: if a student got a mark of 84 in their English class (the class had mean of \(73\) and standard deviation of \(9\)), and a mark of \(79\) in their maths class (class mean of \(70\) with a standard deviation of \(7\)), in which class did the student do better in?
    • For English they were:
      \[ \frac{84-73}{9} \approx 1.22 \mbox{ standard deviations from the mean.} \]
    • For Maths they were
      \[ \frac{79-70}{7}\approx 1.29 \mbox{ standard deviations from the mean.}\]
    • Therefore, the student did better in maths.