Quartiles

In my class we jump 451 centimetres in long jump. Our class is the best! - Oh, your class is good! But I can only jump 406 centimetres. I'm terrible at long jump. But Leon, one person's result can’t give you a view of the class overall.

And it can’t tell you how good you are at jumping compared to the others in your class. To get a better idea, we can do this: Start by sorting the jumps in order of size. Now we will see which jump divides all the jumps into two equal parts. Strike, in pairs, the shortest jump and the longest. Repeat until we have one value left.

Now it is just 339 centimetres left, in the middle. This value is the median. It tells us that half of the class jumped longer, and the other half shorter. But this is only one value, a measure of central tendency. It doesn't say anything about those jumping longer or shorter.

How close to 339 centimeters are they? To find out, we can do this: The median divides all values into two equal parts. We can do the same with the two parts and divide them into two more parts. Start with the jumps that are shorter than the median. Strike in pairs, the shortest and the longest jumps until only 257 and 295 remain.

Here there are two values left. When there is an even number of values, there will eventually be two values left. The median for this part is between the two values. We get that median by adding the values and dividing them by two. It is 276.

Now the eight shortest jumps are split into two equal groups with that median. In the same way, we now divide the longest jumps in the class. Strike the largest and the smallest value in pairs. 392 and 406 remain. The median for this part is between the two values.

That is 392 plus 406 divided by two, which is 399. Now we have three medians. This is getting messy. How do we know which median we’re talking about? When you divide in this way, into four groups, the three values that divide the groups are called quartiles.

The median for the group with shorter long jumps is quartile one, sometimes shortened to q1. The median for all the jumps is quartile two, shortened to q2 and the median for the group with longer jumps is quartile three — q3. The difference between quartile three and quartile one is called the interquartile range. So, the interquartile range for Leon's class is 399 minus 276. That’s 123.

The interquartile range indicates that the spread of jumps among the students who jump closest to the median, is 123 centimetres. So, not everyone in Leon's class jumps 451 centimetres. There is actually a pretty big spread, or dispersion. The interquartile range is a measure of dispersion. So, Leon, a fairer picture of your class results is that most people jump between 276 and 399 centimetres.

Four jump shorter. Four jump longer, and you are one of the students who jumps the longest. Well, okay, that's great. Yes, you sure are! This is proved by the statistics.