Suggested answer to exercise: Arm circumference of students, 6

Question 6: From the graph, approximately what would you estimate the mean and the standard deviation to be? Where would they appear along the horizontal axis?

Suggested answer

The mean will be higher than the median, because the distribution is positively skew. We would expect it to be greater than the 260 estimated for the median, perhaps about 270 mm.

To estimate the standard deviation, we know that about 95% of observations will be within two standard deviations of the mean and that the 5% outside this will be mostly, if not all, at the higher end of the distribution. There are 120 students, so only six would be expected to be outside the limits. There looks to be three above 340 mm and more than this between 320 and 340, so we might estimate four standard deviations as being from the lowest arm circumference to 330, that is from 200 to 330 or 130 mm. A quarter of this is 32.5, so we could estimate the standard deviation to be about 33 mm.

In fact the mean is 270 mm and the standard deviation is 31 mm, so my estimates were good. If you got within 10 mm for the mean and 5 mm for the standard deviation, that was good.

This is how they appear on the histogram:

See detailed description at d. d

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Last updated: 31 July, 2006.

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