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S1 - Standard deviation question, please help! watch

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    I'm really stuck on this question and i've got my exam tomorrow, (its OCR S1 maths btw):

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

    E(x-10) = 208 and E(x-10)^2 = 2716

    i) calc the st.dev of the 20 scores.

    ii) show that Ex^2 = 8876

    iii) 2 other students took the test later. Their scores were 18 and 16. Find the mean and st.dev of all 22 scores

    I've got no idea, please help!
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    (Original post by BobMalouchy)
    I'm really stuck on this question and i've got my exam tomorrow, (its OCR S1 maths btw):

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

    E(x-10) = 208 and E(x-10)^2 = 2716

    i) calc the st.dev of the 20 scores.

    ii) show that Ex^2 = 8876

    iii) 2 other students took the test later. Their scores were 18 and 16. Find the mean and st.dev of all 22 scores

    I've got no idea, please help!
    1. let y=x-10
    .:. Ey=208 Ey^2=2716

    SD = sqrt (Ey^2/20) - (Ey/20)^2

    SD = sqrt (2716/20) - (208/20)^2
    = 5.257

    2. E(x-10)^2 = 2716

    SD = sqrt E(x)^2/20 - (208+20x10/20)^2
    443.796 = E(x)^2/20
    .:.E(x)^2= 443.796x20
    =8876

    3. E(x) = 408 + 18 + 16
    =442
    .:. new mean = 442/22 = 20.1

    E(x)^2 = 8876 + 18^2 + 16^2
    = 9456
    SD = sqrt 9456/22 - 20.1^2
    =5.080
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    Ah, I see! Thanks I get it now!
 
 
 
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