Categorical Data: Can 9 of 20 Beat 14 of 50?

Full transcript

Word for word what is said in the video — the same text as the subtitles. Times are minutes:seconds into the video.

0:00A column you cannot average ▶

The art club is getting hoodies: twenty members, three colours, yellow, red and purple. Every member picks one, so the sign-up list is a column of twenty colours. You can't average purple, so what can you do with a column like this? Three things, and one question that keeps you from being fooled when groups are compared.

0:22The bigger count wins? ▶

When two groups are compared, it is tempting to look at the two counts and pick the bigger one. More votes, more fans, more hoodies: the longest bar looks like the winner, and that feels like a fact. Sometimes it is, but a count on its own can point at the wrong winner, and soon you will see it happen.

0:38Count, then divide: proportions ▶

The first thing you can do is count: how many members picked each colour. Nine picked purple, six went for yellow and five for red, twenty in total. The second thing is to divide each count by that total, which gives a proportion, usually written as a percentage. Nine out of twenty is forty-five percent, six is thirty and five is twenty-five. Together they make a hundred, because every member is counted once. Draw each count as a bar, and you have a bar chart of a category.

1:07The most common answer: the mode ▶

The third thing is the most common answer, and in the art club that is purple, the longest bar. For a category, that answer has a name: the mode. The mode is the colour itself, purple, not the number nine. And the most common answer doesn't have to be what most people picked. Nine members picked purple, but eleven picked something else. Keep those nine purple hoodies in mind, because a second club is about to choose.

1:32Which club likes purple more? ▶

Now the music club picks from the same hoodies, and it has fifty members. Fourteen of them pick purple, against nine in the art club. Pick your answer before the bars move: which club likes purple more?

1:46Out of how many? ▶

Fourteen is more than nine, so the music club, it seems. But first ask the one question that matters here: out of how many? Nine out of twenty is forty-five percent, almost half of the art club. Fourteen out of fifty is twenty-eight percent, just over a quarter of the music club. Not one answer changed, and yet the winner flipped: the art club likes purple more. A count tells you how many, and a proportion tells you how many out of how many. So before you compare two groups of different sizes, ask: out of how many?

2:17Show the count and the total ▶

So should you only ever show percentages? Not quite, because a percentage hides something too. Forty-five percent sounds big, but here it is only nine people. So show both: nine of twenty, forty-five percent. And watch the total itself: say five more members joined the art club but never picked one. Is purple now nine out of twenty, or nine out of twenty-five, which is thirty-six percent? Both are nine hoodies, so always say which total you divided by.

2:47Which order for the bars? ▶

Colours have no order of their own, so you can sort the bars by size, with the longest bar first. In the music club that puts yellow in front, with twenty-one out of fifty. Sizes are different: extra small, small, medium, large and extra large come in an order. Sort those bars by size, and you get medium, large, small, extra large, extra small. The order is gone, so sizes keep their own order, even when the longest bar ends up in the middle. Maybe you saw the question under the last video, about shirt sizes: they are a category, with an order.

3:22Pie chart or bar chart? ▶

The same counts can also go in a pie chart instead of bars, like the music club here. Which slice is bigger, red or purple? In the pie it is hard to tell. As bars on one line it is easy: fifteen for red and fourteen for purple. A pie works best with a few pieces of one whole, where you want to see about a half or a quarter. And it only works when the pieces add up to everyone, with every member counted once. If some people picked two different colours, the shares would add up to more than a hundred percent.

3:53One look back ▶

Back to the fun run, where the team column couldn't be averaged. So which team is the mode of that column? Count it: two gold, three red and three purple, so red and purple share the top. A column can have two modes, and that is still an honest answer.

4:09In one picture ▶

So, in one picture: you cannot average a category, but you can count it. Divide each count by the total for a proportion, and the most common answer is the mode. And before you compare two groups, ask the one question: out of how many,

4:24Next time ▶

because a bigger count is not always a bigger share. Next in the course: what if a column holds amounts instead, like times or heights? Then you count them in ranges, and the width of those ranges can change the whole story. And if you have seen two groups of different sizes compared by their counts, tell me in the comments where. And if you want to keep learning, subscribe, the next video will find you. Until then: happy learning.