Subject: math
Name: Sam
Who are you: Parent (All)

How do you find the median in a group of numbers?


Hi Sam.

The median is the middle value. So you sort the numbers, then choose the one that appears in the middle. For example if the group of numbers is 1, 19, 2, 0, 16, then in sorted order the numbers are 0, 1, 2, 16, 19 and hence the median is 2. If the collection of numbers is even, say 1, 2, 16, 19 then the median is the average of the middle two, so in this case that is (2 + 16)/2 = 9.

Medians are particularly important when means (averages) are skewed by a few numbers that are wildly different from the rest. A mean is found by adding the group of numbers and dividing by the count. So the mean of 1, 19, 2, 0, 16 is 7.6.

For a practical example, let's say that you want to understand the average annual family income for the world. If a report says that the"average" family income is $19,000, that would have to come from the mean, not the median. It doesn't tell us anything about the distribution of values. The most common annual family income (mode) would probably be well under $1,000 because a great many people in the world live on under $2 a day. But since a small number of people are extremely wealthy, when we calculate a mean, we get a figure that is much larger, but perhaps not as informative about most people. That's a confusion a lot of people make.

Statistics also use something called "standard deviation" from the mean which tells us how clustered the numbers are near the mean. A small standard deviation value tells us that the mean is a good representation of most of the numbers (or people) in the data set. A large standard deviation tells us that there is substantial disparity, so the mean shouldn't be interpreted as representing a "typical" case.

Stephen and Penny