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Standard Deviation and Variance

The standard deviation (abbreviated as s or SD) is the average amount of variability that a set of scores contains and is the average distance from the mean. The larger the standard deviation, the more variability is in the set of data and the farther the average point is from the mean of the set of scores.

The formula for computing the standard deviation is as follows:

where

  • s is the standard deviation
  • Σ is sigma, which tells you to find the sum of what follows
  • X is each individual score
  • X¯ is the mean of all the scores
  • n is the sample size.

The variance is simply the square of the standard deviation.

Given the following data set,

  • 56
  • 42
  • 44
  • 67
  • 78
  • 76
  • 56
  • 45
  • 65
  • 61

the steps for computing the standard deviation are as follows. See Table 1 for the corresponding ...

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