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?

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:

See detailed description at d. d

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