To the Outside Observer

In 1999 the government said it wanted to gradually eliminate child poverty. It set itself the goals of reducing child poverty by a quarter by 2005, half by 2010 and altogether by 2020.

In March, the government announced it had narrowly missed its first target, managing to reduce poverty levels by about a fifth rather than a quarter.

Yesterday, the Joseph Rowntree Foundation stated the government may miss its child poverty target unless it changes its approach to boosting the incomes of the poor.

Well what is poverty? The way the government defines it: 60% of median earnings.

Now, I'm no Mathematician, but is it not the case that in any given set of numbers, if we order them one will always (by its very definition), have a median with equal distribution either side.?

Would a more accurate metric of relative poverty be 60% of the mean.?

Well, let's start by making the (not unreasonable) assumption that the UK enjoys a standard distribution, so if we have the following arbitrary ordered set:

10, 10, 15, 18, 25, 45, 150

The median (midpoint) is 18
The mode (most occurrences) is 10
The mean (average) is (10+10+15+18+25+45+150 / 7) is 39

Yet 39 doesn't appear in our set; averages don't have to, they are calculated with reference to the set members, and that's why they can be DANGEROUS and certainly INVITE COMPARISONS!!

5/7ths of our set members are less than average (over 71%)

Assume these figures represent 000's in annual incomes (10,000 15,000 etc)
The poverty stricken 60% of the median (as our government defines poverty) applies to all those earning less than 10,800 which is the two lowest numbers in our set, 2/7ths of the sample, or over 28%

Now, if we were to use the mode, the poverty definition would apply to all those earning less than 6,000. We have no 6 in our sample. So in a simple step I have eliminated 'poverty' from my sample.

What about the mean.? 60% of 39 (our calculated average) is 23.4, so turning this back into our 000's of income; 23,400

4 members of our sample fall under this, 4/7ths, or just over a whopping 57%

"That's great, but what's your point.?"

By using the same set of numbers, I have been able to manipulate perception by changing my method of calculation:

Using 60% of the median (as the government): >28% in poverty
Using 60% of the mode: 0% in poverty
Using 60% of the mean: >57% in poverty

I do long for a system of government that supplies its benefactors raw data for analysis as opposed to the fashion for keeping the mathematical illiterati spoon-fed with junk information. It's the salt 'n' sugar packed soylent-yellow foodstuff of the targets game.

How long before the government announces it's exceeded its target.? How long 'til the next election.?