Math question (statistics) College?

Question

Can anyone help me figure out how to find the Standard DEviation for a set of number. Any set and some instructions on it.

Answer 1

For sample st.dev and sample variance:
the equation for st.dev is the square root of the variance

If the variance is not given, then you have to find that first
that equation is
s^2 = 1/(n-1) {∑xi ^2 - 1/n (∑xi) ^2}
Where xi are your data points
and n is the number of data points.

if given data points 2,4,6,8,10
then
2,4,6,8,10 are your xi
and n=5

First find the values of the sum of your xi and xi ^2
∑xi=2+4+6+8+10 , therefore ∑xi = 30
∑xi ^2 = 4+16+36+64+100 , therefore ∑xi ^2 = 220

now for the equation...
s^2 = 1/(n-1) {∑xi ^2 - 1/n (∑xi) ^2}
= 1/(5-1) {220 - 1/5 (30) ^2}
=1/4 {220 -1/5 (900)}
=1/4 (220-180)
=1/4 (40)
s ^2 =10
so, the std. deviation is the square root of 10
which would be 3.16227766017

Hope that helps
:)

Answer 2

4+4=2

Answer 3

1 2 3 4 5

sqrt (sum (x^2) - sum(x) ^2/n) /(n-1)))

55- 15^2/5 = sqrt(55-45) / 4)

sqrt(2.5) = s.d.

or

sqrt(sum( x-xbar) / (n-1))

xbar = 3

(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2

4 + 1 + 0 + 1 + 4

sqrt(10/4) = sqrt(2.5)