# Suggested answer to exercise: Heights 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?

The mean will be close to the median, because the distribution is symmetrical. We would expect it too to be about 1650 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 about equally at both ends of the distribution. There are 120 students, so only six would be expected to be outside the limits. There looks to be two or three in lowest height interval and one in the highest, so we expect our four standard deviation range to be a bit less than 1800 – 1500 = 300, say about 280 mm. A quarter of this is 70, so we could estimate the standard deviation to be about 70 mm.

In fact the mean is 1658 mm, slightly above my estimate, a nd the standard deviation is 70 mm. I was spot on. It is difficult to judge accurately from the histogram. If you got within 20 mm for the mean and 10 mm for the standard deviation, that was good.

This is how they look on the histogram:

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