# Another Impossible Question (Edexcel S1, Q5)

Discussion in 'Mathematics' started by D Franklin, Jan 18, 2012.

1. ### D Franklin

Question is about correlation between variables t,w. It's w I'll be concentrating on here.

You're given n = 10, \sum w = 111.75, S_ww = 0.16. You're later told one value was an outlier, with w = 20.

The question asks you to explain, without calculation, what happens to the correlation when you remove the outlier. The "standard answer" is that there's more correlation.

However, if you actually do the calculations, it decreases (*). Moreover, you find S_ww becomes negative (which is of course impossible).

(*) I haven't checked this bit myself. I have checked that S_ww becomes negative.

2. ### valed

I doubt that - perhaps you mean 'stronger' ?
Have you really? Without knowing sum of w&sup2; ?
Now that would be impressive!

3. ### Polecat

'Have you really? Without knowing sum of w&sup2; ?'
I have to agree with D.Franklin as far as S_ww is concerned.
The 'before' value is too small if w=20 is one of the included values.
I found the before value of sigma(w^2) = 1250.40625.

4. ### D Franklin

Possibly; it's been 20 years since I did stats and I care more about principles than nomenclature.
Not really - there is, of course, a simple relationship linking S_ww, \sum w^2 and \sum w.

5. ### valed

DF
1
Why worry about nomenclature? Yes, why? It only matters if you are trying to understand what is happening!!!!
2
The simple relationship is known generally but in this specific case, I would LOVE to see your calculation .... you know, if it's that simple, even someone out of touch for 20 years should be able to explain it to little old me

6. ### Polecat

'2
The simple relationship is known generally but in this specific case, I would LOVE to see your calculation .... you know, if it's that simple, even someone out of touch for 20 years should be able to explain it to little old me. '
Are you saying you disagree with the result of the calculation or that you can't be bothered.? I worked it through, and agree with DF. Please correct me.
Why should posters be expected to think you don't know things clearly given in the formula booklet.
At least the sun is shining.

7. ### D Franklin

I must confess, I get a slightly different value for w^2 than you; my calculation is at http://www.thestudentroom.co.uk/showpost.php?p=35917136&postcount=86 for what it's worth.

In any event, it makes no difference to whether the new s_ww is negative; in either case the original variance is impossibly low if there's supposed to be such a severe outlier of a sample.

8. ### valed

I did all the calculations and came to similar results but I don't see the point of the thread when the question clearly states 'without further calculation'. These calculations took longer than merited 2 marks.
I didn't!

9. ### Polecat

But surely the point made by the OP is that the question was based
on impossible data. I haven't seen the complete question, but I
assume the dodgy part has been correctly reported.

10. ### D Franklin

Precisely. I doubt it will have directly affected people taking the exam, but I think it's pretty bad practice on the part of the examiners.

You can actually spot the problem without detailed calculation. From the given data, E[ w] = 11.175, so if one same actually had a value of 20, that immediately tells you s_ww = \sum (w_i - E[ w])^2 has to be a lot more than 0.16.

11. ### ColinWilson

Students happy to just put in the numbers and write down the results will have no problems with this question. However, more able students could well have problems if they actually understand Statistics. They could have wasted a lot of time trying to work out why the numbers just dont add up.
There is no need to work out SUM w^2 as
Sww = (20--11.175)^2+ ......= Rather more than 0.16 !
An error of around 50000 % on an A-Level Maths paper is beyond belief !

12. ### D Franklin

Yes. It's a long time since I've done a regression question in anger, and I was basically skimming the question to check what I'd already been told about the problem. But even so, I had a feeling of "y'know, that value for s_xx seems impossibly small".

That was what I was getting at in the last paragraph of my previous post.
Watch Edexcel say "well we *told* you not to use calculation. Now see what you've done!".

13. ### PiranhaStar commenter

Stats is not my thing, but (ignoring the error that's been discussed at length) don't you need to know what value of t corresponds to w=20 to know what happens to the correlation? Or does "outlier" refer to distance from the least square line or something similar?

14. ### Anna-Luise

It was given in the question which you can see here if you're curious.

15. ### AnotherMathsHoD

I also raised it with Ofqual and had the same response - I also raised it with Edexcel who said they would pass it to the Mathematics team, and that I would receive a reply once the grade boundaries have been set.

16. ### GoldMathsNew commenter

Anyone teaching D1 - a lot of pupils seem annoyed with the minimum route inspection Q2 on last weeks paper. It didnt state starting and finishing at same point (it is however assumed in the algorithm) not knowing this 1 "small" fact could potentially cost 7 marks! In previous papers it has always been stated.

17. ### pwc9000New commenter

There has been some mention of this. But I think they should know the algorithm is starting and finishing at the same point and is only adjusted to starting and finishing at different points if specifically instructed. I can't imagine a "correct" solution for starting and finishing at different points is going to cost anywhere near 7 marks though.

18. ### Guzintas

Agree that this is a disappointing response, I would go further and say it is pathetic. So much for the new Ofqual with teeth. What are they playing at?

19. ### Polecat

Well, Ofqual have been informed, so I would like to think that if the board does not report what they intend to do about it, then there should be serious consequences for an individual or two.
Surely, when all such errors are detected, the first people to be informed should be the subject officers at the relevant board, with a copy to Ofqual. Hopefully that will ensure compliance with the rules of the game.
The BBC and other media may very well be interested, but I think they should only be brought in if the board is off-putting..

20. ### DMNew commenter

It isn't always easy to find out who to contact at a particular Awarding Body. They don't tend to publicise the address of their Exam Mistakes Department.