Big Dog 04 Posted January 21, 2005 Share Posted January 21, 2005 Hey can anyone tell me the formulae for finding the standard deviation of a probability distribution? Been looking but dont seem able 2 find out thx Quote Link to comment Share on other sites More sharing options...
Econ Posted January 21, 2005 Share Posted January 21, 2005 Hey BD 04: Say that x1, x2, x3, x4, x5, ...., xn are n draws from a (random) sample. Then: Step 1: Compute the mean, i.e. m =[ Sum xi (i=1,..., n) ] / n Step 2: Compute the squared deviation of each observation from its mean, i.e. For x1 --------> (x1-m)^2 For x2---------> (x2-m)^2 ..... For xn---------> (xn-m)^2 Step 3: The variance is V= [(x1-m)^2 + (x2-m)^2 + .... + (xn-m)^2 ] / n Step 4: The s.d. is s.d. = V^(1/2) Example: Let x1=10, x2= 20 and x3=30 Then: (1) m=20 (3) V = [ (10-20)^2 + 0 + (30-20)^2] / 3 = 200/3 (4) s.d. = (20/3) ^ (1/2) Quote Link to comment Share on other sites More sharing options...
Dingus Posted January 21, 2005 Share Posted January 21, 2005 To sum up : Standard Deviation is a positive root of the mean of the sum of the squares of the deviations of the individual values, taken from the arithmetic mean. :) OR as an aid to remember: Standard Deviation is the positive root-mean-square value. Quote Link to comment Share on other sites More sharing options...
Big Dog 04 Posted January 21, 2005 Author Share Posted January 21, 2005 I dont think you understood the question exactly so maybe an example would clarify it. How would you find the sd below without having to write the numbers out individually? Thx 4. Find the standard deviation for x, given the frequency distribution below. x f 0 2 1 6 2 3 3 2 4 4 Quote Link to comment Share on other sites More sharing options...
Dingus Posted January 21, 2005 Share Posted January 21, 2005 In that case, you calculate it as follows: Short Method: sqrt [Σfidi^2 / Σfi - (Σfidi/Σfi) ^2)] Where--> di --> Deviations from the arbitrary/assumed/working mean (Xw)--> X - Xw fi --> frequency of xi In this case: Let us assume that the working mean (Xw) is : 2 So di = X - Xw = -2, -1, 0, 1, 2 Σfidi = -2*2 + -1*6 + 0*3 + 1*2 + 2*4 = -4 + -6 + 0 + 2 + 8 = 0 Therefore second fraction within the root is ZERO. First fraction: Σfidi^2 8 + 6 + 0 + 2 + 16 = 32 Σfi = 17 Therfore Standard Deviation = sqrt 32/17. So approximating: S.D. is slightly less than sqrt 2 or S.D. 2 Quote Link to comment Share on other sites More sharing options...
Big Dog 04 Posted January 21, 2005 Author Share Posted January 21, 2005 Thank you sir you are right - now i just need 2leanr the formula Quote Link to comment Share on other sites More sharing options...
peterv Posted January 22, 2005 Share Posted January 22, 2005 Is standard deviation within the objectives of the GRE? Quote Link to comment Share on other sites More sharing options...
jayashri_rane Posted January 22, 2005 Share Posted January 22, 2005 Hey Bigdog, also check the mathreview from the gre.org website. You can find it with powerpep software also, which has math review button. In that you will find all topics which can appear on gre math section. http://www.gre.org/pracmats.html Quote Link to comment Share on other sites More sharing options...
Big Dog 04 Posted January 22, 2005 Author Share Posted January 22, 2005 Jayashri i got the question from the Math review lol Quote Link to comment Share on other sites More sharing options...
kts Posted January 24, 2005 Share Posted January 24, 2005 I did the "finding SD for freq distribution sum" using this formula and I found this one quite easy: SD=sqr root of(E [f(x-mean)^2]/N) create 3 additional columns for the sum like this: First calculate the mean. mean=0(2)+1(6)+2(3)+3(2)+4(4)/17= 34/17 = 2 x f (x-mean) (x-mean)^2 f(x-mean)^2 0 2 -2 4 8 1 6 -1 1 6 2 3 0 0 0 3 2 1 1 2 4 4 2 4 16 ---------- E[f(x-mean)^2]= 32 ----------- a)SD= sqr root of(E [f(x-mean)^2]/N)= sqr root of(32/17)=1.4 approximately b)Mode=x with highest frequency=1 c)median=2 d)range=biggest x - smallest x=4-0=4 This entire sum took me 2 minutes to do. I hope the above expln. will make u understand better. Quote Link to comment Share on other sites More sharing options...
kts Posted January 24, 2005 Share Posted January 24, 2005 separate the 5 column numbers under their heading. I typed it in a tabular form but i guess the browser ignores spaces. Column 1 heading=x Column 2 heading=f Column 3 heading=(x-mean) column 4 heading=(x-mean)^2 column 5 heading=f(x-mean)^2 Add the numbers of the 5th column to get the number 32. Quote Link to comment Share on other sites More sharing options...
Big Dog 04 Posted January 30, 2005 Author Share Posted January 30, 2005 thx kts- it has clarified it Quote Link to comment Share on other sites More sharing options...
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