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Standard Deviation

  • By: Bruce Frey
  • In: Encyclopedia of School Psychology
  • Edited by: Steven W. Lee
  • Subject:School/Educational Psychology (general), School Psychology, Educational Psychology

Standard deviation (SD) is the average distance of each score in a distribution from the mean. It is calculated by squaring the difference between each score and the mean, averaging those squared differences, and taking the square root of that average. Operating under an assumption of a normal distribution of scores, the mean and standard deviation can be used to make probability statements about the likelihood of the occurrence of any individual score and to estimate the proportion of a population that will perform above, below, or between given score levels. For example, approximately 5% of students will score above or below 1.96 standard deviations from the mean in a normal distribution. In measurement, the standard error of measurement is assumed to be the standard ...

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