Stats 1 question: standard deviation

[whitefeather]

I missed the lesson on this and i can't figure out how to do this question with the data given.

Homework Statement

A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by:
∑(x-10) = 208 and ∑(x-10)² = 2716

i) calculate the standard deviation of the 20 scores.
ii)show that ∑x² = 8876
iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.

Homework Equations

unsure

The Attempt at a Solution

I tried i, ∑(x-10)² / 20 =varience = 2716/20
standard deviation =√(2716/20)= 11.65
I think this is wrong though because 10 isn't the mean.

 

[Ray Vickson]

I missed the lesson on this and i can't figure out how to do this question with the data given.

Homework Statement

A class of 20 students takes a test. The score, x , for each student was recorded by the teacher. The results of summarised by:
∑(x-10) = 208 and ∑(x-10)² = 2716

i) calculate the standard deviation of the 20 scores.
ii)show that ∑x² = 8876
iii) Two other students took the test later. Their scores were 18 and 16. Find the mean and standard deviation of all 22 scores.

Homework Equations

unsure

The Attempt at a Solution

I tried i, ∑(x-10)² / 20 =varience = 2716/20
standard deviation =√(2716/20)= 11.65
I think this is wrong though because 10 isn't the mean.

So, you need to find the mean. Alternatively, you can just look at y = x-10 instead of x. How are the variance of x and the variance of y related?

RGV