# Stats 1 question: standard deviation

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.

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
Homework Helper
Dearly Missed
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.

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