Example 2

Describing a Data Set

 

The dot plot shows the average numbers of hours students in a class sleep each night. Describe the center and the variation of the data set.

Most of the data values are on the right, clustered around $$9$$, and the tail extends to the left. The distribution is skewed left, so the median and the interquartile range are the most appropriate measures to describe the center and the variation.

The median is $$8.5$$ hours. The first quartile is $$7.5$$, and the third quartile is $$9$$. So, the interquartile range is $$9 - 7.5 = 1.5$$ hours.

The data are centered around $$8.5$$ hours. The middle half of the data varies by no more than $$1.5$$ hours.

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