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Suggested answer to exercise: Alcohol consumption from the 2005 questionnaire, 3

Question 3: Would you expect the median to be greater or less than the mean?
From the graph, approximately what would you estimate the median and the mean to be?

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Suggested answer

The distribution is highly skew to the right.
We would expect the median to be less than the mean.

Judging from the graph, the median would be just above 5,
because the height of the first bar is almost equal to the
sum of the heights of all the other bars combined.
We might expect this to be 6 units/week.
The mean would be greater, somewhere towards the top of the interval 5 to 10.
We might estimate the mean to be 8 units/week.

In fact the median is 5 units/week.
The digit preference leads there to be several observations equal to 5,
which are all at the start of the interval 5 to 10 units/week.
The mean is 7.9 units/week.

This is how they appear on the histogram:

d

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Last updated: 12 October, 2006.

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