The news says prices rose 4% this year. But rent rose 10% and bread rose 2%. Nobody paid exactly 4% more for anything. One number is standing in for thousands of price tags. This lesson shows how that number is made.
Rent50%
Bread50%
Start with just two things to buy. Say people spend half their money on rent and half on bread. Rent rose 10%. Half of that is 5. Bread rose 2%. Half of that is 1. Add the two halves. The figure is 6%.
Rent50%
Bread50%
Same two things, still half and half. This year rent rose 8% and bread rose 2%. What is the figure?
%
Take half of each rise and add them.
Right. Half of 8 is 4, and half of 2 is 1. Each rise counts for exactly half, because each thing takes exactly half of the money.
Rent is 20p of every £13.6%
Rent is 80p of every £18.4%
The figure, when rent rose 10% and everything else rose 2%.
Now change the shares. If rent takes 20p of every £1 spent, rent's 10% rise only counts for a fifth. If rent takes 80p of every £1, it counts for four fifths. The word for this kind of average is a weighted average. The weights are the shares of spending.
Rent rose 10% and everything else rose 2%. Move the control to change how much of people's spending goes on rent.
Rent rose10%
Everything else rose2%
The inflation figure3.6%
Share of spending on rent: 20%
Rent still rose 10% and everything else still rose 2%. The figure is 3.6%.
Rent rose10%
Everything else rose2%
The inflation figure5.2%
Share of spending on rent: 40%
Rent still rose 10% and everything else still rose 2%. The figure is 5.2%.
Rent rose10%
Everything else rose2%
The inflation figure6.8%
Share of spending on rent: 60%
Rent still rose 10% and everything else still rose 2%. The figure is 6.8%.
Rent rose10%
Everything else rose2%
The inflation figure8.4%
Share of spending on rent: 80%
Rent still rose 10% and everything else still rose 2%. The figure is 8.4%.
Rent's rise never changed. What made the inflation figure move?
Everything else catching up.
Not yet. Everything else stayed at 2% throughout. The third bar climbed while the first two stood still.
How much of people's spending goes on rent. That is the weight.
Right. Same two rises, four different figures. The only thing that moved was the share of money going to the thing that rose most.
Rent getting dearer.
Not yet. Rent rose 10% in every frame. Look at the first two bars: neither of them moved.
Move the control.
Four price rises in one year, with how much of each pound people spend on them. Tap the one that moves the figure MOST.
Tap the part of the picture that answers it.
Multiply each rise by its share of spending.
Rent — 30p of every £1 spent5%
Eggs — 1p of every £140%
Petrol — 6p of every £115%
Eating out — 10p of every £18%
How much each price rose.
Rent
Right. A 5% rise on 30p of every pound adds 1.5 points to the figure. A point here means one per cent. The smallest rise here is the biggest mover, because of its weight.
Eggs
Not yet. Forty per cent is the biggest rise and the smallest mover. On 1p in the pound it adds 0.4 of a point. A huge rise on a tiny share makes the news, but it barely moves the figure.
Petrol
Not yet. Fifteen per cent on 6p in the pound adds 0.9 of a point. Second place, and it feels bigger than that because everyone sees the price on a sign.
Eating out
Not yet. Eight per cent on 10p in the pound adds 0.8 of a point. Close to petrol, and well behind rent.
Bread
++
A haircut
++
A phone bill
++
A bus fare
Four of the roughly 700 kinds of thing in the basket.
The real figure is made the same way, only with far more things. The UK's statistics office picks about 700 kinds of thing that people buy, from bread to haircuts to phone bills. That list is called the basket. Every month, somebody has to go and find the price of each thing in it.
How many separate prices does the UK's statistics office check each month to make the figure?
Pick one. Nothing is scored.
Kinds of thing in the basket700
Prices checked each month180,000
About 180,000.Most people guess far lower. Each of the 700 kinds of thing is priced in many shops and towns, so one loaf of bread is hundreds of prices. Then every rise is weighted by what households spend on it, and the whole month becomes one number.
Put the recipe in order: from price tags to one number.
Tap them in the order they happen, first to last. Each tap gets a number.
Choose the basket→Collect the prices→Work out each rise→Weight by spending→One number
Right. The weighting step is the one people forget. It is also the one people argue about most, because a different set of weights gives a different number from the same prices.
A pint of beer9%
The whole basket3%
A newspaper says: inflation is 3%, but a pint of beer has gone up 9%, so the official figure must be wrong. What is the newspaper missing?
The figure is out of date.
Not yet. It is calculated every month from that month's prices. Being a month old is not what makes it differ from the pint.
Beer is not in the basket.
Not yet. It is. The basket is built from what people actually buy, and beer is on the list. But beer is one small item among 700, so its 9% barely moves the average.
One price can rise far more than the average without the average being wrong. Beer is a small share of spending.
Right. The figure is an average of 700 things. It does not say what any one of them did. Some of the 700 rose more than 9%, and some fell.
Lesson complete
The inflation figure is one average. Each price counts by how much people spend on it.