Range (statistics)

Every day on their way to and from school, Lina and Leon pick up plastic bags that they find littering the path. After a month, they compare how many they have found. Here is Leon’s result... ...and here is Lina’s. They calculate how many bags they found on average per day. Leon adds all his results... ...

a total of 50 bags. And then he divides the number by 25 school days. That is an average of exactly two bags per day. Lina also calculates how many bags she found per day. She was sick for four days and didn’t go to school, so she counts the 21 days she was well.

She found 42 bags in 21 days. This will be the same average as Leon’s, exactly two bags per day. Well, it was a draw. I don't understand. There were so many days when you came home without any bags!

Yes, for 15 of the 25 days, Leon did not find a single bag. But it was the same average! How did this happen? Aha, here it is: one day, Leon found a whole roll of plastic bags, 37 pieces! And that was what raised the result for Leon’s average, the mean.

Just calculating the mean does not give the whole picture of how much effort they put in, Lina thinks. She wants to calculate something other than the mean. Which shows that Leon found many plastic bags on a single occasion, but for the most part did not find any bags at all. One way is to look at the difference between the highest result for a single day and compare it with the lowest result for a single day. Lina found four bags at most and no bags at least.

The difference, or variation, in Lina’s result is then four minus zero, equal to four. For Leon, the variation is 37 minus zero, that's 37. The variation between the highest and the lowest value is called range. Lina’s result has a range of four and Leon’s a range of 37. A high value for the range indicates that there is a large spread of values in a survey.

And a small range that there is a small spread. Range is a measure of dispersion. What happens if we remove the 37 bags that Leon found in one day? Leon's results get a mean of 13 bags divided by 24 days, that’s a little more than only half a bag per day. His result gets a range that is only two minus zero, equal to two.

That the range is changed from 37 to two just by deleting a single result shows that 37 is a very unusual result. Leon's results have a much larger spread than Lina’s. But Lina had a much more equal result, every single day. So, if you had continued to collect plastic bags for another month, Lina would probably have found more bags than Leon. Let’s do it another month!

Well, I don’t know... You won't be as lucky next time! Come on, the most important thing is not that anyone won, but that you tidied up the school path.