Jelly beans and the art and science of statistics

When you think of statistics what comes to mind?

a) lots of numbers in tables and charts?

b) difficult equations about combinations and permutations and probability?

c) jelly beans?

Yes, jelly beans.

They’re great for showing how to do stats without lots of numbers or tricky equations. I use them a lot in my workshops. Jelly beans, and glue and glitter, ping-pong balls, toy cars, games of snakes and ladders …

But for this posting I’m going to talk about jelly beans.

Here are two bags bought at the same time…

Unopened-jelly-beans-in-bowls

They’re from Sainsbury’s but you can choose which ever store you like.

Let’s open them up – but don’t eat them … yet!

Beans-emptied-into-bowls

Without counting how would you work out which bag has more beans in total?

Well, one way is to put them back into the bags – or into the bowls in this case – on a ‘one for you, one for me’ basis.

Here’s one from the A pile into Bowl A and one from the B pile into Bowl B…

One-A-beanOne-B-bean

Here’s another in Bowl A and another in Bowl B…

Two-A-beansTwo-B-beans

… and so on until one or other load of beans (or both) runs out.

In this case the B bag had more beans…

More-B-beans-than-A

Let’s take a deeper look at the B beans.

They’re different colours. But there seem to be more of some colours than others.

Which colour beans are most? Again, you can find out without counting.

Let’s visualise our jelly bean data – that’s the art bit – with a jelly bean bar chart…

B-bean-bar-chart

(For some great visualisations check out David McCandless’s site.)

It looks like the purple-ish beans have the edge over the orange beans. To be sure we can put them into purple-orange pairs…

Paired-up-beans

Yes, purple had the advantage. I had to pair two purples at the end – they’re in the centre.

Did you spot the lonely bean?

Funny-colour-bean

Is it a colour all by itself or just a yellow one with a glitch?

How would you classify it? Would others agree? Even with jelly beans there can be issues about classification or categorisation.

Here are some more questions we can ask about our beans before we eat them…

  • What about the A beans? We know that there are fewer beans. But would we find the distribution of the colours the same as the B beans?
  • What would be our expectations of other bags? In a way these bags are samples from the Great Jelly Bean Universe. How many bags would you open before you became confident of the proportions you’d tend to expect?
  • And, if you’re the manufacturer how much does it matter that bag A had fewer than bag B? What does this say about the process controls you have in place?

We didn’t have to count anything or use any complicated formulas to get going with statistical thinking.

If you would like to be more confident when working and communicating with basic statistics – whether or not you have thoughts on jelly beans! – contact me to discuss your needs.

Finally, they’re very tasty but you might like to check the calories before eating a whole bag in one go …!

Jelly-bean-calories

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