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Suggested answer to exercise: Arm circumference of students, 5

Question 5: From the graph, approximately what would you estimate the median
and the first and third quartiles to be?
Where would they appear along the horizontal axis?

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Suggested answer

The median is the value which divides the distribution into two equal parts.
The middle of the distribution looks to be just above 260 mm.

The first quartile, which cuts off the bottom quarter of the observations,
would be somewhere near the lower end of the tallest bar,
in the 240 to 260 mm interval, perhaps around 245 mm.
The third quartile, which cuts off the top quarter of the observations,
appears to be in the 280 to 300 mm interval, perhaps around 290 mm.

In fact, the median is 262.5 mm, the first quartile is 249.5 mm
and the third quartile 287.5 mm.
Of course, it is difficult to judge accurately from the histogram and
any answers within 10 mm of the correct one are good.

This is how they look on the histogram:

d

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Last updated: 19 January, 2009.

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