EXAMPLE 1 Finding the median

We might compare Bonds’s career with that of Hank Aaron, the previous holder of the career record. Here are Aaron’s home run counts for his 23 years in baseball:

13 27 26 44 30 39 40 34 45 44 24 32
44 39 29 44 38 47 34 40 20 12 10

To find the median, first arrange them in order from smallest to largest:

10 12 13 20 24 26 27 29 30 32 34 34
38 39 39 40 40 44 44 44 44 45 47

The bold 34 is the center observation, with 11 observations to its left and 11 to its right. When the number of observations is odd (here ), there is always one observation in the center of the ordered list. This is the median, .

269

How does this compare with Bonds’s record? Here are Bonds’s 22 home run counts, arranged in order from smallest to largest:

5 16 19 24 25 25 26 28 33 33 34
34 37 37 40 42 45 45 46 46 49 73

When n is even, there is no one middle observation. But there is a middle pair—the bold 34 and 34 have 10 observations on either side. We take the median to be halfway between this middle pair. So Bonds’s median is