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Standard Deviation Tutorial

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Standard Deviation Definition:
     Standard deviation is a statistical measure of spread or variability.The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean.

Variance Definition:
     The square of the standard deviation. A measure of the degree of spread among a set of values; a measure of the tendency of individual values to vary from the mean value.

  Formula:

Standard Deviation
standard deviation formula
  Population Standard Deviation
      population standard deviation 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.

XM(X-M)(X-M)2
13-24
23-11
3300
4311
5324


  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.

XX2
11
24
39
416
525


  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

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

  Perform the steps 1 and 2 as seen in above example.

  Step 3:Now find the population standard deviation using the formula.
            √10/√5 = 1.414

  Variance Example: To find the Variance of 1,2,3,4,5.

  After finding the standard deviation square the values.
            (1.58113)2 = 2.4999

  Same for Population standard deviation.
            (1.414)2 = 2



Related Calculator:
>> Standard Deviation Calculator.

This tutorial will help you dynamically to find the standard deviation problems.