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Properties of Standard Deviation

  1. The standard deviation of first n natural numbers 1, 2, 3, …, n is 95153.png.
  2. The variance and consequently standard deviation of a distribution is independent of change of origin.
  3. The variance or standard is not independent of change of scale.
  4. If all the values of the variable are same, then standard deviation is zero.
  5. The standard deviation does not alter when a constant quantity k is added to or subtracted from each value of the variable of the series.

Some more properties

  1. For a symmetrical distribution
    Mean ± 0.6745 covers 50% of items
    Mean ± 1 σ covers 68.27% of items
    Mean ± 2 σ covers 95.45% of items
    Mean ± 3 σ covers 99.93% of items
  2. The sum of squares of deviations of items in the series from their arithmetic mean is minimum.
  3. QD = 2/3σ, MD = 4/5σ, and QD = 5/6MD.
  4. Coefficient of mean deviation = MD/Median × 100%.
  5. Coefficient of variance = σ/mean × 100%.
  6. Sometimes a graph of cumulative frequency is called an ogive, obtained by plotting the cumulative frequencies against the end points of the class intervals.

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