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s1 math question watch

1. pls help

a class of 20 students takes a test. the score, x, for each student was recorded by the teacher. the results are summarised by:

sumof(x-10)=208
sumof(x-10)^2=2716

show that sumofx^2=8876

how?
2. (Original post by MiniBarSmarties)
pls help

a class of 20 students takes a test. the score, x, for each student was recorded by the teacher. the results are summarised by:

sumof(x-10)=208
sumof(x-10)^2=2716

show that sumofx^2=8876

how?
You have 20 people and all their results are recorded, but 10 points is taken off their scores and added together, to give you 208. (That means the sum of x is 208+20x10 = 408)
Then when you're calculating sigma (x-10)
(x-10)(x-10) = x^2 + 100 - 20x
If you do this for 20 separate x values, you will have sigma x^2, 2000 more than you want and 20 lots of sigma x less than you want.
therefore:-2716=sigmax^2 + 2000 - 20 x 408
sigmax^2 = 8876
Katie
3. (Original post by Katie Heskins)
You have 20 people and all their results are recorded, but 10 points is taken off their scores and added together, to give you 208. (That means the sum of x is 208+20x10 = 408)
Then when you're calculating sigma (x-10)
(x-10)(x-10) = x^2 + 100 - 20x
If you do this for 20 separate x values, you will have sigma x^2, 2000 more than you want and 20 lots of sigma x less than you want.
therefore:-2716=sigmax^2 + 2000 - 20 x 408
sigmax^2 = 8876
Katie
Thank You
4. (Original post by Katie Heskins)
(x-10)(x-10) = x^2 + 100 - 20x
If you do this for 20 separate x values, you will have sigma x^2, 2000 more than you want and 20 lots of sigma x less than you want.
therefore:-2716=sigmax^2 + 2000 - 20 x 408
sigmax^2 = 8876
Katie
i dont understand this step though? why is 408 put in?
5. oh dont worry ive worked it out now!!!!
thanks again
i was a bit slow to realise but its sorted now!

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