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S1 questions help!

So I've been given this information:
Sum of (x-10) = 208
Sum of (x-10)^2 = 2716
n=20
How am I supposed to use this to show that the sum of x^2= 8876 ?
Thank you
Reply 1
Also stuck on the next part of the question XD
'Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.'
I'd really appreciate any help! Thank you!
Reply 2
Original post by phoebeg76
So I've been given this information:
Sum of (x-10) = 208
Sum of (x-10)^2 = 2716
n=20
How am I supposed to use this to show that the sum of x^2= 8876 ?
Thank you


This is a coding question.

which square is the latter one? is it:
(\sum x)^2 \text{or} \sum x^2
Reply 3
Original post by lerjj
This is a coding question.

which square is the latter one? is it:
(\sum x)^2 \text{or} \sum x^2


It's the second one, without brackets!
Reply 4
Original post by phoebeg76
It's the second one, without brackets!


Caluclate the standard deviation of the coded data- what affect does adding and subtracting have on standard deviation?

Calculate the actual value for x\sum x using the coded value and the value for n.

(sorry if that doesn't work, you're actually three pages further into S1 than I am :frown:)
Original post by phoebeg76
So I've been given this information:
Sum of (x-10) = 208
Sum of (x-10)^2 = 2716
n=20
How am I supposed to use this to show that the sum of x^2= 8876 ?
Thank you


It may be easiest to do this from basics - you can expand those sums:

Unparseable latex formula:

\sum (x-10)^2 = \sum (x^2-20x+100)\\[br] =\sum x^2 -\sum 20 x+\sum 100



Etc. And you know this equals 2716.

Do something similar with the other one.

Don't forget, since n=20, 100=20×100\sum 100 = 20\times 100
Reply 6
Original post by ghostwalker
It may be easiest to do this from basics - you can expand those sums:

Unparseable latex formula:

\sum (x-10)^2 = \sum (x^2-20x+100)\\[br] =\sum x^2 -\sum 20 x+\sum 100



Etc. And you know this equals 2716.

Do something similar with the other one.

Don't forget, since n=20, 100=20×100\sum 100 = 20\times 100


okay.. I still don't understand how this helps me to find out the sum of x^2?
Some more help please? Sorry - I'm just really stressed and sleep deprived so this isn't making much sense to me right now!
Original post by phoebeg76
okay.. I still don't understand how this helps me to find out the sum of x^2?
Some more help please? Sorry - I'm just really stressed and sleep deprived so this isn't making much sense to me right now!


You have:

2716=x220x+1002716=\sum x^2-\sum20x+\sum 100

which contains the term you're looking for.

You know what the last term is. You just need to find what 20x\sum20x is.

So do something similar with the (x10)=208\sum(x-10)=208 to find that.
Reply 8
Original post by ghostwalker
You have:

2716=x220x+1002716=\sum x^2-\sum20x+\sum 100

which contains the term you're looking for.

You know what the last term is. You just need to find what 20x\sum20x is.

So do something similar with the (x10)=208\sum(x-10)=208 to find that.


okay thank you so much I've found an answer! I really hate 'show that' questions, never sure of the correct method!
Reply 9
Original post by ghostwalker
You have:

2716=x220x+1002716=\sum x^2-\sum20x+\sum 100

which contains the term you're looking for.

You know what the last term is. You just need to find what 20x\sum20x is.

So do something similar with the (x10)=208\sum(x-10)=208 to find that.


So I've (finally) figured out that question (thank you so much for that by the way). I was just wondering if you could possibly help me with the next part of the question that I'm also stuck on!
'Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.'
I'd really appreciate any help! Thank you!
Original post by phoebeg76
So I've (finally) figured out that question (thank you so much for that by the way). I was just wondering if you could possibly help me with the next part of the question that I'm also stuck on!
'Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.'
I'd really appreciate any help! Thank you!


Well you now know n, sigma x and sigma x^2 for the original number of 20 students.

All you need to do is adjust those values for the additional scores, and apply the formulae for the mean and sd.
(edited 9 years ago)

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