Notnek learns stats

Reply 60

Gregorius

14

Original post by Notnek

I think I'm starting to like stats :ninja:

Welcome to the dark side, my friend, muahahahahaha! :mwuaha:

It's still not one of my favourite areas of maths but with my teaching hat on I can appreciate that there are some nice areas for discussion. Although I'm really not a fan of the silly topics where there is no universal agreement like for example how to find quartiles from discrete data.

Oh, no kidding!

Reply 61

Physics Enemy

19

Original post by Gregorius

I think this is a very telling thought about statistics taught at A-level. Perhaps the problem here is ...

I think reforms along with tweaking specs over the years contributed to a skewed perception. Recent specs I've looked at are filled with pointless junk/tests.

There used to be more (tough) prob/comb/perm Qs. I have an old OCR S1 book that's quality; many tough/deep 'starred' problems that really get you thinking.

It developed this area of my thinking/maths e.g) able to do Cam test Qs. Also came in handy when playing card games and the odd casino outing. :wink:

(edited 6 years ago)

Reply 62

Notnek

OP

21

Exponential models / regression lines:

Answer for b:

"b is the rate of change of g per degree".

Is this correct? I interpret this as saying that the rate of change of g is constant but it isn't.

I think if I was answering this I would say something like : "For an increase in temperature by 1 degree, the growth rate increases by a factor of b".

Reply 63

DFranklin

18

Original post by Notnek

Answer for b:

"b is the rate of change of g per degree".

Is this correct? I interpret this as saying that the rate of change of g is constant but it isn't.

I think if I was answering this I would say something like : "For an increase in temperature by 1 degree, the growth rate increases by a factor of b".

You've got to hate people who set questions like this. I disagree with their answer, if I was answering I'd probably say "b is the growth rate of g per degree". (and grit my teeth at the annoyance of writing this when g is itself a growth rate).

[FWIW, I personally feel your answer falls a little into "mathematically correct but maybe not advancing understanding", but it's a damn sight better than the "rate of change of g per degree"].

Reply 64

Notnek

OP

21

Original post by DFranklin

You've got to hate people who set questions like this. I disagree with their answer, if I was answering I'd probably say "b is the growth rate of g per degree". (and grit my teeth at the annoyance of writing this when g is itself a growth rate).

[FWIW, I personally feel your answer falls a little into "mathematically correct but maybe not advancing understanding", but it's a damn sight better than the "rate of change of g per degree"].

Thank you. I probably should have been sure that the book's answer was wrong since this is not stats specific knowledge but I still don't have that confidence yet!

My style of answer came from looking at other textbook answers where they like to compare the change in the dependent variable to an increase of 1 in the independent variable. So I suppose my answer was an A Level stats style answer :smile:

Reply 65

atsruser

11

Original post by Notnek

Exponential models / regression lines:

Answer for b:

"b is the rate of change of g per degree".

Is this correct? I interpret this as saying that the rate of change of g is constant but it isn't.

I think if I was answering this I would say something like : "For an increase in temperature by 1 degree, the growth rate increases by a factor of b".

1) I don't like their model eqn much: we really need

g=ab^{\lambda t}

to ensure that the exponential is dimensionless, and then set

\lambda =1

maybe. But that's by-the-by

2) Note that

g(t+1)=ab^{t+1}=b(ab^t)=bg(t)

. In other words, if we increase t by 1, we multiply

g(t)

by a factor b, which agrees with what you said.

3) The "rate of change of g per degree" to my mind presumably must be interpreted as the average rate of change per degree, since

g'(t)

is clearly not constant i.e. it is given by

\frac{\text{rise}}{\text{run}} = \frac{g(t+1)-g(t)}{1} = bg(t)-g(t)=(b-1)g(t) \ne b

. So their description strikes me as incorrect, if taken in any kind of literal sense (which mathematician types tend to do...)

Reply 66

atsruser

11

Original post by DFranklin

You've got to hate people who set questions like this. I disagree with their answer, if I was answering I'd probably say "b is the growth rate of g per degree".

I'd say "g increases by a factor of b for each 1 degree increase in temperature". [edit: which is pretty much how notnek worded it, of course]

The original wording is dismal.

Reply 67

Notnek

OP

21

Stats in A Level maths was pretty easy to relearn so I thought I'd give further maths stats a go. There's a good chance that I'll have questions.

If this goes well maybe I'll even be able to tackle stats questions in STEP!

(edited 6 years ago)

Reply 68

Notnek

OP

21

If anyone's interested in the FM topics I'll be attempting to (re)learn:

Permutations/combinations/probability - (I won't need to relearn this but I'll do a lot of questions to familiarise myself with them)
Probability distributions for discrete RVs
Discrete uniform distribution
Geometric distribution
Poisson distribution
Continuous RVs, PDFs, CDFs
Combinations of RVs
Central limit theorem
Unbiased estimates of population mean and variance
Hypothesis tests for a population mean using the normal distribution
Confidence intervals
Contingency tables
Fitting a theoretical distribution
Goodness of fit test
Non-parametric tests
Basis of sign tests, Wilcoxon tests
Single-sample,two-sample and paired-sample hypothesis tests
Spearman's rank including hypothesis tests
Linear regression

Reply 69

Notnek

OP

21

Five women and four men stand in a line.

a) In how many arrangements will all the men be apart?
b) In how many arrangements will all the men be apart and all the women be apart?

For a) I got the same answer as the book. For b) it seemed pretty simple and I did 4! x 5! = 2880. But the answer in the book is 5760.

I can't see any problem with my method so I'm hoping it's an answer mistake. Can someone please check if they agree with mine or the book's answer (or something else)? I can post my thinking if people don't agree.

Thanks!

Original post by Notnek

Five women and four men stand in a line.

a) In how many arrangements will all the men be apart?
b) In how many arrangements will all the men be apart and all the women be apart?

For a) I got the same answer as the book. For b) it seemed pretty simple and I did 4! x 5! = 2880. But the answer in the book is 5760.

I can't see any problem with my method so I'm hoping it's an answer mistake. Can someone please check if they agree with mine or the book's answer (or something else)? I can post my thinking if people don't agree.

Thanks!

They can be arranged as:

Man, Woman, Man, Woman, ....

or

Woman, Man, Woman, Man, ....

You found the possibilities for only one of the two cases.

Reply 71

Notnek

OP

21

Original post by RDKGames

They can be arranged as:

Man, Woman, Man, Woman, ....

or

Woman, Man, Woman, Man, ....

You found the possibilities for only one of the two cases.

But if the list starts with a man then you have

MWMWMWMW...

At this point you run out men so two women would be next to each other?

Original post by Notnek

But if the list starts with a man then you have

MWMWMWMW...

At this point you run out men so two women would be next to each other?

Ah, didn't think about the arrangements in full to spot that.
In which case, I agree with your answer.

Reply 73

ghostwalker

17

Original post by Notnek

For a) I got the same answer as the book. For b) it seemed pretty simple and I did 4! x 5! = 2880. But the answer in the book is 5760.

Agree with 2880.

Reply 74

Notnek

OP

21

Original post by RDKGames

Ah, didn't think about the arrangements in full to spot that.
In which case, I agree with your answer.

Original post by ghostwalker

Agree with 2880.

Thanks!

Reply 75

Notnek

OP

21

I'm a bit rusy with all this:

For n objects where there are

r_A

of type A,

r_B

of type B etc. the number of permutations of all objects is

\displaystyle \frac{n!}{r_A!\cdot r_B!...}

E.g. how many arrangements are there of the letters MATHEMATICS. This is simply:

\displaystyle \frac{11!}{2!\cdot 2!\cdot 2!}

Now what if the question was, "How many four letter words can you make from MATHEMATICS?". I'm thinking that there's no set formula* to do this kind of thing and the question requires analysis of the ways you can group the repeated letters.

Is this right? Or is there a quicker way to do this kind of question?

*well not a commonly used one anyway.

Reply 76

ghostwalker

17

Original post by Notnek

I'm a bit rusy with all this:

For n objects where there are

r_A

of type A,

r_B

of type B etc. the number of permutations of all objects is

\displaystyle \frac{n!}{r_A!\cdot r_B!...}

E.g. how many arrangements are there of the letters MATHEMATICS. This is simply:

\displaystyle \frac{11!}{2!\cdot 2!\cdot 2!}

Agreed.

Now what if the question was, "How many four letter words can you make from MATHEMATICS?". I'm thinking that there's no set formula* to do this kind of thing and the question requires analysis of the ways you can group the repeated letters.

Is this right? Or is there a quicker way to do this kind of question?

*well not a commonly used one anyway.

Agreed - no set formula.

I can see it done as 3 cases:

Spoiler

(edited 6 years ago)

Reply 77

Notnek

OP

21

Original post by ghostwalker

Agreed.

Agreed - no set formula.

I can see it done as 3 cases:

Spoiler

Thanks again, yes this is the way I did it.

I'm not sure if counting problems like this were anywhere in the old maths/further maths - I don't remember doing any.

Reply 78

ghostwalker

17

Original post by Notnek

Thanks again, yes this is the way I did it.

I'm not sure if counting problems like this were anywhere in the old maths/further maths - I don't remember doing any.

I think they're getting a bit more adventurous.

Back in my day, of 4-figure tables and sliderules, the only stats. was a different A-level "Maths and Stats", which I didn't do.

Reply 79

Notnek

OP

21

Original post by ghostwalker

I think they're getting a bit more adventurous.

Back in my day, of 4-figure tables and sliderules, the only stats. was a different A-level "Maths and Stats", which I didn't do.

I'm not sure I'd class this type of question as stats although it's easy to turn one of these questions into a probability question which links to stats. Edexcel have this topic in the pure section whereas OCR have it in stats.

Tables are still used in old spec stats which seems a bit "back in my day". The new spec requires calculators instead of tables for a lot of questions but many teachers don't want to change :smile:

Notnek learns stats

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you