# Properties of Standard Deviation

- The standard deviation of first
*n*natural numbers 1, 2, 3, â€¦,*n*is . - The variance and consequently standard deviation of a distribution is independent of change of origin.
- The variance or standard is not independent of change of scale.
- If all the values of the variable are same, then standard deviation is zero.
- 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

- For a symmetrical distribution
- The sum of squares of deviations of items in the series from their arithmetic mean is minimum.
- QD = 2/3Ïƒ,
*=*4/5Ïƒ, and QD = 5/6MD. - Coefficient of mean deviation = MD/Median Ã— 100%.
- Coefficient of variance = Ïƒ/mean Ã— 100%.
- Sometimes a graph of cumulative frequency is called an
*ogive*, obtained by plotting the cumulative frequencies against the end points of the class intervals.