S1 exam paper help!

Can someone help with this question please? I have part (ai) right but I don't know why I then didn't get the rest of the question right...I subbed in my answers to convert them and they were wrong. I don't get part (b) either



I'm going through a past paper and I've only just started revising stats so I'm probably going to end up asking for help on most questions

I'll do my best to help you through..

a)i) Just check the value of your mean again..
a)ii) This tests your knowledge of what the mean and standard deviation of a data set really are, do you know? If not then we can work off that basis..

I got the mean=62.25 then subbed it in and got the new mean to be 16.81 which is right now but can you explain part (aii) please?

a)i) Yeah thats the mean i got aswell
a)ii) Okay here's my explanation...

The mean of a set of data is basically the sum of all the terms divided by how many. The standard deviation of a set of data is the average distance from the mean.

Let me give you an example:

Consider the data set: 1 2 3 4 5
Obviously, the mean is 3 (the sum is 15, divide by 5 and you get 3)
The standard deviation (which you can use your fancy formula for) would give a result of sqroot(2) i.e 1.4142.... What this tells us is the average distance from the mean. (i wont go into great detail as to why here)

What about if we add 5 to each of those numbers so: 6 7 8 9 10

Well clearly the mean has changed, it is now 8, so its just the previous mean + 5
But the standard deviation has not changed because all we've done is shift the numbers along a bit, the average distance from the mean hasn't changed!

What about if we multiplied all the numbers by 2: 2 4 6 8 10
Well now, again, the mean has changed. It is now 6. It is 2 x the previous mean.
This time the standard deviation has changed (it has doubled) because we have changed the average distance from the mean by scaling all the numbers.

So in summary,
If we want to use coding:
-The mean will be a coded value, that is if we multiply it by some number then shift it (+/- some other number) the mean will change accordingly like in the above example
-The standard dev. is NOT affected by shifting the data, because the average distance from the mean stays the same, BUT it is affected by scaling.

Hopefully this makes some sense...

So, your question:
a)ii) c = 5/9(f) + 160/9 by expanding the brackets.

The mean IS affected by this coding, that is if we sub in the mean into that formula, we will get the new mean according to that "code" (you have done this correctly)
But the standard deviation is not affected by that shift factor "+160/9" at the end, so for the standard deviation we require:
coded standard dev. = 5/9(old standard deviation)
This should give the correct answer.

Any more questions about what ive explained/any more confusion with the paper please don't hesitate to ask, statistics can be an abstract topic (one of the reasons I prefer mechanics!) but also extremely interesting and definitely applicable in the real world..

Hope I helped..

s1 is pretty hard compared to S3
S3 is just hypo tests like krushkall Wallis but I'm dead for S1 exam as I didn't pay attention at the start of the year

I don't have to do s3 only s1 I'm not doing stats A level its just one of my modules for maths, I couldn't cope with the whole of stats. I don't get it at times because it seems to be more put these numbers in your calculator rather than understand whats going on

s1 is pretty hard compared to S3
S3 is just hypo tests like krushkall Wallis but I'm dead for S1 exam as I didn't pay attention at the start of the year