278 Part 4: The State of the World
DEFINITION
The median of a set of data is the middle value when the data are ordered from
smallest to largest. If the data set contains an even number of values, the median is
the average of the two middle values.To find a median, you just need to put the data in order and find the value that falls exactly in
the middle of the list. If there is an even number of data points, and two numbers seem to be in
the middle, the mean of those two numbers is the median. If the data set is very large, sorting
and counting to find the middle can be tedious, and that’s a good time to use a computer to help
with the task. But for smaller data sets, finding the median is fairly simple.
Suppose a class of 10 students earned the grades below on an exam.
78, 59, 92, 82, 74, 97, 63, 75, 66, 88
To find the median grade, put the grades in order. Usually, people sort from low to high, but high
to low will work, too.
59, 63, 66, 74, 75, 78, 82, 88, 92, 97
There are 10 grades, so the median will be the average of the fifth and sixth grades. Counting in
from the low end, the fifth grade is 75 and the sixth is 78. The median is (75 + 78) z 2 =
153 z 2 = 76.5. The median grade is 76.5.
Earlier you found the mean number of acres of land in parks and wildlife areas for eight states in- To find the median of the same data, first put the list in order by acreage.
Land in Rural Parks and Wildlife Areas 2002 (1,000 acres)
Minnesota 2,959
Michigan 1,436
Wisconsin 1,000
Missouri 649
Illinois 432
Ohio 372
Iowa 327
Indiana 264The median will be the average of the fourth and fifth values. (649 + 432) z 2 = 1081 z 2 =
540.5 thousand acres or 540,500. Remember that the mean was 929,875 acres. The mean is larger
than the median because it’s pulled toward the large acreage for Minnesota. The median doesn’t
get pulled in the same way, which is why statisticians say that the median is resistant.