The quartiles of any distribution are the values with cumulative proportions 0.2

Question

The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. The interquartile range IQR is the distance between the rst and third quartiles of a distribution. a) What is the value of the IQR for the standard Normal distribution? b) There is a constant c such that IQR = c for any Normal distribution N(; ). What is the value of c? c) The percent of observations that are suspected outliers according to the 1:5 IQR rule is the same for any Normal distribution. What is this percent?

Explanation / Answer

Look up the Z value corresponding to 0.75 and you'll get between 0.67 and 0.68 (let's say 0.675). That means 0.75 of the probability density is below 0.675. Since a normal distribution is symmetric around zero, that means 0.25 of it is below -0.675. So the IQR is 0.675 - (-0.675) = 1.35

For a normal distribution, = 1, so c = IQR / = IQR = 1.35
Since you've been told c is a constant, that means c is always 1.35

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