Statistics Part 1, the Muffins Story

What are statistics good for?

Imagine you own a bakery and you have to figure out how many chocolate muffins you should cook per day.

So you go and talk to the chef:

You: How many muffins did we sold last week?
Chef: 77
You: Ok.
You(think): so if we sold 77 muffins in a week, i just need to calculate the average for each day
and i will know how many muffins we have to cook! So 77 in 7days(77/7=1), is 11 per day!
You: please cook 11 per day.
Chef: So many? are you sure?
You(think): Well, why not?, i calculated the average per day, everybody knows that the average is the
correct way to go, what could be wrong??
You: Yes im sure! cook 11!
... FAIL...


What could be wrong?

Example 1

If the amount of muffins sold per day was like this:

{ monday:10, tuesday:11, wednesday:12, thursday:9, friday:13, saturday:11, sunday:11 }

Then if you do an average:

(10+11+12+9+13+11+11)/7=11

You get 11 per day. And by looking at the daily results it is reasonable to expect that you will sell around 11 per day in future. All cool.

Example 2

But what really happened is that last week, was that on friday, there was a school visit to the bakery so the real amount of muffins sold per day, or all the week, were:

{ monday:2, tuesday:3, wednesday:1, thursday:2, friday:68, saturday:1, sunday:0 }

Thus, doing the average:

(2+ 3+ 1+ 2+ 68+ 1+ 0)/7=11

The average is 11 per day, so should the chef cook 11 per day? No! You can clearly see that baking 11 will be too much, even thought thats what average says!! So sometimes a simple average does not tells the whole store and thats what statistics are for, to avoid these mistakes and be to able to calculate reliable predictions.

Hope that give some motivation into why learning statistics is useful.

This is part 1 of 3, part 2 is here and part 3 here.