3- Understanding Standard Deviation

Ankit Gupta
Sep 9, 2018 · 2 min read

Deviation means how far from the normal.

Standard Deviation- The Standard Deviation is a measure of how spread out numbers are from the mean. It’s denoted by symbol σ (the Greek letter sigma)

Population Standard Deviation- It is the square-root of population variance

Population Standard Deviation

Sample Standard Deviation- It is the square-root of sample variance

Sample Standard Deviation

Properties of standard deviation

When using standard deviation keep in mind the following properties.

  • Standard deviation is only used to measure spread or dispersion around the mean of a data set.
  • Standard deviation is never negative.
  • Standard deviation is sensitive to outliers. A single outlier can raise the standard deviation and in turn, distort the picture of spread.
  • For data with approximately the same mean, the greater the spread, the greater the standard deviation.
  • If all values of a data set are the same, the standard deviation is zero (because each value is equal to the mean).

When analysing normally distributed data, standard deviation can be used in conjunction with the mean in order to calculate data intervals.

If x bar = mean, σ= standard deviation and x = a value in the data set, then

about 68.2% of the data lie in the interval: mean-σ < x < mean + σ.
about 95.4% of the data lie in the interval: mean-2 σ < x <mean + 2 σ.
about 99.6% of the data lie in the interval: mean -3 σ < x < mean + 3 σ.

Source- Wikipedia

Credits:- statcan.gc.ca

Ankit Gupta

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Ex Credit Suisse, Ex HSBC | My need for Freedom dominates my decisions | Want to go everywhere

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