# standard deviation

Discussion in 'General Education' started by sjcgirl07, Sep 23, 2009.

1. ### sjcgirl07Companion

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Sep 23, 2009

Does anyone know how to find the standard deviation from a set of scores. I am really confused by this.

3. ### kcjo13Phenom

Joined:
Dec 6, 2005
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Sep 23, 2009

I'm stretching to remember this...Alice, help...it is tedious:

First, find the mean for the set. For each value (x) in your set, subtract the overall mean from x, then multiply that result by itself (otherwise known as determining the square of that value). Add up all those squared values. Then divide that result by the number of values in the set, minus 1 (n-1). Then, find the square root of that last number.

Or, you could just enter the values into Excel, and use the STDEV or STDEVP formula, which would be a lot easier!

Or, you could get yourself a good scientific calculator!

4. ### AliceaccMultitudinous

Joined:
Apr 12, 2006
Messages:
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Sep 23, 2009

You did well kc!!!

Here's a site that explains with an example: http://easycalculation.com/statistics/learn-standard-deviation.php

"Formula:

Standard Deviation

Population Standard Deviation

(OOPS, IT'S NOT SHOWING THE FORMULA!!)

where Σ = Sum of
X = Individual score
M = Mean of all scores
N = Sample size (Number of scores)

Variance :

Variance = s2

Standard Deviation Method1 Example: To find the Standard deviation of 1,2,3,4,5.

Step 1: Calculate the mean and deviation.
X M (X-M) (X-M)2
1 3 -2 4
2 3 -1 1
3 3 0 0
4 3 1 1
5 3 2 4

Step 2:Find the sum of (X-M)2
4+1+0+1+4 = 10

Step 3:N = 5, the total number of values.Find N-1.
5-1 = 4

Step 4:Now find Standard Deviation using the formula.
√10/√4 = 1.58113

Standard Deviation Method2 Example: To find the Standard deviation of 1,2,3,4,5.

Step 1:First, square each of the scores.

X X2
1 1
2 4
3 9
4 16
5 25

Step2: Use the formula
s = square root of[(sum of Xsquared -((sum of X)*(sum of X)/N))/(N-1)]
= square root of[(55-((15)*(15)/5))/(5-1)]
= square root of[(55-(225/5))/4]
= square root of[(55-45)/4]
= square root of[10/4]
= square root of[2.5]
s = 1.58113"

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Sep 23, 2009

thanks

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