Page 90 - Statistics for Dummies

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Part II: Number-Crunching Basics
is called the median. The median is still an unsung hero of statistics in the
sense that it isn’t used nearly as often as it should be, although people are
beginning to report it more nowadays.
The median of a data set is the value that lies exactly in the middle when the
data have been ordered. It’s denoted in different ways; some people use M
and some use . Here are the steps for finding the median of a data set:

1. Order the numbers from smallest to largest.
2. If the data set contains an odd number of numbers, choose the one

that is exactly in the middle. You’ve found the median.
3. If the data set contains an even number of numbers, take the two

numbers that appear in the middle and average them to find the
median.
The salaries for the Los Angeles Lakers during the 2009–2010 season (refer to
Table 5-2) are ordered from smallest (at the bottom) to largest (at the top).
Because the list contains the names and salaries of 13 players, the middle
salary is the seventh one from the bottom: Derek Fisher, who earned $5.048
million that season from the Lakers. Derek is at the median.
This median salary ($5.048 million) is well below the average of $7.029 million
for the 2009–2010 Lakers team. Notice that only 4 players of the 13 earned more
than the average Lakers salary of $7.029 million. Because the average includes
outliers (like the salary of Kobe Bryant), the median salary is more representa-
tive of center for the team salaries. The median isn’t affected by the salaries of
those players who are way out there on the high end the way the average is.
Note: By the way, the lowest Lakers’ salary for the 2009–2010 season was
$959,111 — a lot of money by most people’s standards, but peanuts com-
pared to what you imagine when you think of an NBA player’s salary!
The U.S. government most often uses the median to represent the center with
respect to income data again because the median is not affected by outliers.
For example, the U.S. Census Bureau reported that in 2008, the median house-
hold income was $50,233 while the mean was found to be $68,424. That’s quite
a difference!
Comparing means and
medians: Histograms
Sometimes the mean versus median debate can get quite interesting.
Suppose you’re part of an NBA team trying to negotiate salaries. If you
represent the owners, you want to show how much everyone is making
and how much money you’re spending, so you want to take into account

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