Variance and Standard Deviation

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Variance: Variance is a measurement of spread or dispersion of observations within a given dataset. Variance measures how far each observations is from mean. Dispersion of data gives the variability around the central tendency and can be calculated by the difference between largest and smallest value within dataset also known as range.

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Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.

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But there is a major problem with variance and that is the difficulty of interpreting the units of variance. How does one interpret squared percents, squared dollars, or squared yen? This problem is mitigated through the use of the standard deviation. The standard deviation is the square root of the variance and is calculated as follows:

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Advantages of Standard Deviation:

  1. Shows how much data is clustered around a mean value
  2. It gives a more accurate idea of how the data is distributed
  3. Not as affected by extreme values
  4. Good estimate of variation of a data set if the distribution is normal

Disadvantages of Standard Deviation:

  1. It doesn’t give you the full range of the data

 

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