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The ages of 12 runners in a recent marathon are listed.

24, 16, 30, 14, 19, 31, 23, 33, 15, 31, 19, 27

Find the median and interpret its meaning as it relates to the runners.

The median is 19.5, and it represents the typical age of the runners.
The median is 23.5, and it represents the typical age of the runners.
The median is 25.5, and it represents the difference in the lowest and highest ages of runners.
The median is 28.5, and it represents the difference in the lowest and highest ages of runners.

1 answer

To find the median of the ages of the 12 runners, we first need to arrange the ages in ascending order:

14, 15, 16, 19, 19, 23, 24, 27, 30, 31, 31, 33

Since there are 12 ages (an even number), the median will be the average of the 6th and 7th values in the ordered list.

The 6th and 7th ages are:

  • 6th: 23
  • 7th: 24

Now we calculate the median:

\[ \text{Median} = \frac{23 + 24}{2} = \frac{47}{2} = 23.5 \]

Thus, the median age of the runners is 23.5.

Interpretation: The median represents the typical age of the runners in the marathon, meaning that half of the runners are younger than 23.5 years old, and half are older. This value provides a central point of comparison for analyzing age distribution among the runners.