Sample standard deviationcan be found by taking the positive square root of the sample variance.
Example:Continuing with our example, take the square root of 44.50 = 6.67%
l: Calculate the proportion of items falling within a specified number of standard deviaitons of the mean, using Chebyshev's inequality.
Chebyshev's inequality states that for any set of observations (sample or population, regardless of the shape of the distribution), the proportion of the observations within k standard deviations of the mean is at least 1 - 1/k2for all k > 1. If we know the standard deviation, we can use Chebyshev's inequality to measure the minimum amount of dispersion, regardless of the shape of the distribution.
Chebyshev's inequality states that for any distribution, approximately:

  • 36% of observations lie within 1.25 standard deviations of the mean

  • 56% of observations lie within 1.50 standard deviations of the mean

  • 75% of observations lie within 2 standard deviations of the mean

  • 89% of observations lie within 3 standard deviations of the mean

  • 94 of observations lie within 4 standard deviations of the mean

m: Define, calculate, and interpret the coefficient of variation.