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Suggested answer to exercise: Alcohol consumption from the 2005 questionnaire, 4

Question 4: From the graph, approximately what would you estimate the standard deviation to be?
How would the mean and standard deviation relate to the histogram?

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Suggested answer

The distribution is highly skew to the right.
We would expect all the 5% of observations which are more than two standard deviations
from the mean to be in the upper tail.
This starts at about 25 units/week.
The mean is about 8,
so two standard deviations will be roughly equal to 25 - 8 = 17 units/week.
The standard deviation will be about 17/2 = 8.5 units/week.

In fact, the standard deviation is 8.8 units/week.

The standard deviation is slightly greater than the mean.
One standard deviation less than the mean will be just below zero.

This is how they appear on the histogram:

d

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Last updated: 12 October, 2006.

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