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SecTIoN 1D Describing Quantitative Data with Numbers 49

Measuring center: The Median

In Section 1C, we advised you to simply use the “middle value” in an ordered
quantitative data set to describe its center. That’s the idea of the median.

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DEFINITION Median
The median is the midpoint of a distribution — the number such that about half the
observations are smaller and about half are larger. To find the median, arrange the
data values from smallest to largest.
• If the number n of data values is odd, the median is the middle value in the
ordered list.
• If the number n of data values is even, use the average of the two middle values

in the ordered list as the median.

You can find the median by hand for small sets of data. For instance, here are
data on the population density (in number of people per square kilometer) for all
seven countries in Central America: 65

Country Belize Costa Rica El Salvador Guatemala Honduras Nicaragua Panama
Population density 17 100 308 158 82 48 52
2
(people per km )
To find the median, start by sorting the data values from smallest to largest:
17 48 52 82 100 158 308

Because there are n = 7 data values (an odd number), the median is the middle
value in the ordered list: 82.
Here is a dotplot of the population density data. You can confirm that the
median is 82 by “counting inward” from the minimum and maximum values.
Median

0 50 100 150 200 250 300 350
2
Population density (people per km )

More chips please Skill 2.C
EXAMPLE Measuring center:

The median

PROBLEM: Have you ever noticed that bags of chips seem to contain
lots of air and not enough chips? A group of chip enthusiasts collected
data on the percentage of air in a sample of 14 popular brands of chips.
Here are their data: 66

Ann Heath

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