STANDARD DEVIATION

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STANDARD DEVIATION

• M.Prasad Naidu
• MSc Medical Biochemistry, Ph.D,.

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• It is an improvement over mean deviation
• Measure of dispersion
• Used most commonly in statistical analyses

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Calculation of SD

• First find the mean of series
• Find the deviation or difference of individual
  measurement from mean
• Next find the sum of squares of deviation or
  difference of individual measurements from their
  mean
• Now find the variance (Var) mean squared
  deviation
• var ? (X - X) 2/ n

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Square root of variance that gives SD

• If large sample size
• If sample less than 30

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For ex
Mean 25341/5 15/5 3 Var 10/5 2
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Uses of SD

• It summarizes the deviation of a large
  distribution from mean in one figure used as unit
  of variation
• Indicates whether the variation of difference of
  an individual from mean is by chance
• Helps in finding the SE which determines whether
  the difference between means of two similar
  samples is by chance or real
• Helps in finding the suitable size of sample for
  valid conclusion.

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SD of normal curve

• The shape of curve will depend upon mean and SD
  of which in turn depend upon the number and
  nature of observation.
• In normal curve -
• Area b/w 1 SD on either side of mean will include
  approximately 68 of values in distribution
• Area b/w 2 SD is 95
• Area b/w 3 SD is 99.7
• These limits on either side of mean are called
  confidence limits

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Standard normal curve

• Smooth
• bell shaped
• Perfectly symmetrical
• Based on infinity large number of observation
• Total area of curve 1
• Mean 0
• SD 1
• Mean , median and mode all coincide

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SD of normal curve

• Bell shaped curve will show an inflexion on the
  ascending as well as descending units of curve
• If vertical lines are drawn from each of these
  points they will intersect the X axis on either
  side of the mean at an equal distance from it
• A large portion of area under the normal curve
  has been included in portion of curve b/w the 2
  points of inflexion

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• The distance b/w the mean and point of inflexion
  either side is equal to SD and is denoted by a
  sign prefixed to it to indicate that it extends
  on either side of mean.
• If another vertical line is drawn an either side
  of mean at a distance equal to twice SD most of
  values in distribution table would have been
  included in this part of curve
• In most cases, SD will include 2/3 of sample
  values and mean 2 SD will include 90 of values.

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THANK YOU