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1. 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

2. (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

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
3. Ah, I see! Thanks I get it now!

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