Scores on a psychological test are modelled as having a normal distribution with a mean of 100 and
a standard deviation of 10. Assume that this model is correct and that a random sample of 200
observations is to be obtained.
(a) Indicate values that you would expect to observe for the five-number summary for this sample,
i.e. the minimum, the lower quartile, the median, the upper quartile and the maximum. Clearly
show your reasoning. (3)
(b) Hence, draw a likely boxplot for such a sample (ignore possible outliers). (2)
(c) According to the IQR rule, an observation is labelled as a potential outlier if it is more than
1.5xIQR above the upper quartile, or 1.5xIQR below the lower quartile, where IQR denotes the
inter-quartile range. Show that, for a sample from a normally distributed population the IQR rule
identifies any observation that is more than 2.7 standard deviations from the mean as an outlier.
(2)
a standard deviation of 10. Assume that this model is correct and that a random sample of 200
observations is to be obtained.
(a) Indicate values that you would expect to observe for the five-number summary for this sample,
i.e. the minimum, the lower quartile, the median, the upper quartile and the maximum. Clearly
show your reasoning. (3)
(b) Hence, draw a likely boxplot for such a sample (ignore possible outliers). (2)
(c) According to the IQR rule, an observation is labelled as a potential outlier if it is more than
1.5xIQR above the upper quartile, or 1.5xIQR below the lower quartile, where IQR denotes the
inter-quartile range. Show that, for a sample from a normally distributed population the IQR rule
identifies any observation that is more than 2.7 standard deviations from the mean as an outlier.
(2)