How do you do this S1 question?

I am told to find the standard deviation of this data x 11 13 15 20 25

I know that standard deviation is the square rooting of the variance but how would you go about this bearing in mind in includes x's?

Reply 1

Amber May

what was the standard diviation ? and what exactly are you trying to find out x or the varience?

(edited 10 years ago)

Reply 2

jazzyjay29

you may have to find the standard deviation in terms of x? Unless there's any other information given so that you can actually work out x using that?

Reply 3

hoodboilu4

Sum them all up, you should get something like:

A + x

Where A is a real number.

Then divide that number by the total of numbers of values you have, in your case it is 6 giving you something like this giving you the mean..

\mu = \dfrac{A}{6}+\dfrac{x}{6}

Then for each value from your set of values, subtract the mean and square the value you get. For these set of values, we will call them squared values.

x_1=x, x_2=11, x_3=13 \cdots[br] [br] (x_1-\mu)^2 = (x - (\dfrac{A}{6}+\dfrac{x}{6}))^2[br] (x_2-\mu)^2 = \cdots[br] \cdots[br][br]

Add the squared values all up and then work out the mean of the squared values by dividing by 6... This is your variance...

\sigma^2 = \dfrac{1}{6}((x_1-\mu)^2+(x_2-\mu)^2+(x_3-\mu)^2 +\cdots)[br]

Then square root that value and you have you standard deviation, you should end up with an algebraic equation.

Reply 4

maggiehodgson

I've just been looking at this

http://statistics.about.com/od/Descriptive-Statistics/a/Range-Rule-For-Standard-Deviation.htm

It tells me that you can come up with a good estimate for sd by range divided by 4.

An estimate then would be (25-x)/4

Is that any use to you?