S1 answers Watch

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#1
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Hello dudes. Just done the people just done the S1 paper again. Lifted a copy from school. These are the answers I got.

1.
Easy histogram (with class boundaries between i.e 7.5~8.5)
2.
I got t = 14.52 for life of battery
3a)
Sxy = -157.86
Sxx = 155.92
Syy = 214.96

3b)
PMCC= -0.862 to 3sf

3ci) PMCC unaffected by coding
cii) Strong negative correlation

4a) Proved k = 1/50
b) E(x) = 5.4
Var(x) = 0.52

4c) Var(2x-3) = 4Var(x) = 2.08

5 Dice
a) Uniform Distribution
b)E(x) = 3.5
Var(x) = 35/12
c) P(6,6,6) = 1/216
d)Score 16
6,6,4 6,4,6 4,6,6 5,5,6 5,6,5 6,5,5

So P(16) = 6/216 = 1/36

6a) Mean = 22 and 2/7
b) Unordered then ordered Stem & Leaf
c) Median = 20 , LQ = 13 , UQ = 31
d) IQR = 18 So no outliers
e) Box Whisker
f) Q2-Q1<Q3-Q2 so positive skew

7a) M explanatory
b) Scatter
c) Regression Line: 2.23 + 1.41x
d) Line best fit
e) Approx 23 in Physics if student got 15 in maths

Did everyone else get these or similar?:

Forgive me if there are any mistakes but I thought I would post somke solutions to put people out of their misery. Hope it went well dudes.
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Decided to start a new thread with these answers. I added them to another thread but I thought people might want to see these asap to see if they agree with my solutions. All the best, Dan
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I think I got roughly the same answer, with one exception. I don't think I got the same for question 4 on the expectation and variance. what did everyone else get. I hate those questions so I'm sure I didn't get it right anyway. Scrim
Surfing Hamster
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Can you post the mark allocations for the questions please It'd be great if you could upload or scan and email me a copy!?
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I got all the same apart from Q2 which i put a minus in, i think i lost 6 marks due to careless mistakes!!!
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Sorry friend no scanner I'm afraid.
The marks were
1) 5
2) 6
3a) 4
3b) 3
3c) 2
4a) 3
4b) 6
4c) 2
5a) 1
5b) 3
5c) 2
5d) 4
5e) 2
6a) 2
6b) 3
6c) 3
6d) 3
6e) 3
6f) 2
7a) 1
7b) 3
7c) 8
7d) 2
7e) 2

Hope this helps you out, let me know how you think you got on, all the best, Daniel
Leekey
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I think my Var(x) was different from yours but generally i think i've got decent marks
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I posted the solutions, and the Var(x) one was the only one i was unsure of, so you probably nailed that one. Still I think I did okay considering I ran out of time and couldn't check my work. hope you got it right and got 100%. All the best, Dan
mensandan
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According to Mr hughes site the answer I put for the E(X) Varx was correct which is good news as I thought I had stuffed it, all the best, Dan
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Leekey
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I think that my method was correct so I probably did get the same answer as you and if not, hey, it only a few marks.
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U know for describing the correlation, it's probably worth 2 marks right? I put reasonably strong, negative correlation. Would I get the marks?
Leekey
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Usually....

Recognising the negative gradient = 1 mark
Recognising that 0.8 is quite strong = 1 mark
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For the discrete uniform distribution, I used the method of
E(X)=(n+1)/2 and Var(X)=(n+1)(n-1)/12

I thought that I'd got that question wrong, cos hardly anyone I talked to after the exam had used the method, and I wasn't sure if I'd got the method right. I'm so relieved that it seems that the method was right.(If I was ever to do a question like that, I'll stick to the normal way of doing it, would save me the hassel of worrying so much)
Leekey
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I'll be totally honest and say that I have never come across that way of doing it before!!! I used the conventional way and hopefully I got it right (can't remeber what I got). As long as you got the marks thought mate....thats whats important!!!
mensandan
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I like the method you used. You have used the forulae for the sum of the first n nautral numbers for E(x) and the formula for the first n square numbers to get Var(x)

A very powerful and time saving technique. Most people just work out all the combinations and add, which is fine but imagine if you had a million sided dice in the question. Your method (my method of choice) will get the answer in seconds flat. If I were you I would contiune to use this technique, it is faster an more elegant. You will encounter these results in P1 for the sum of the first n natural numbers and P4 I think for the sum of the first n square numbers. Dan
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Leekey
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#16
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That method is much better than the standard way but for all us tiny minded "need-to-pass-maths-but-hate-it" people, its just easier to use one method for all.

P.S.
A million sided dice - I'd love to see the size of the game board for that one. Can you imagine rolling a 700,984, count the squares on that beast!!!
mensandan
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Hey good point if it works use it and get the marks in the bag. Didn't know that they taught the other method in S1 but it really doesn't matter in the end. Yes a million sided dice would lead to a bizarre game but it was the best analogy I could think of (which is a little sad). S1 is the only Statsa module I will ever do and I am glad about that as I really don't want to learn any more of it, it is really messy and clumsy. Anyone else find that half the books contradict each other (median n/2 or n+1/2, should/shouldn't interpolate) there are reasons but they never explain them properly. The edexcel S1 book made a complete mess of the quartiles/deciles stuff so as to confuse the hell out of me. Anyone actually enjoy S1? I didn't but I do like M1 and P1. Which makes me sad I know. Dan
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Leekey
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I actually don't mind stats. I don't do M1 and I aren't too fond of P1 but stats seems to make sense to me for some reson. I was gutted this year because the test had very little probability which is like my "chosen specialist subject". Thanks for post the marks scheme by the way!!!
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Yup, I got really confused with the quartiles stuff using the text book, cos in some parts you use n+1, in some you don't. In some questions, you round off to find the nth value, and in some, you take the average of the n and n+1th value. Hey, I'm confusing myself even writing this (and probably confusing the rest of you while I'm at it). Anyways, I hope that I did get the value right whichever way I used.
Oh yeah, the methods for the mean and variance of a discrete uniform distribution are under that heading in the text book. I looked at it the night before, and luckily remembered it. The reason why I used it instead of the traditional method, was cos the question was only worth 3 marks, compared to the other qu. of 6/5 marks.
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what exam board was this for??
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