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Statistics

Table of contents

Standard Deviation and Variance

Standard Deviation

  • Standard Deviation is a measure of how spread out numbers are.
# Standard deviation = a measure of how spread out a group of numbers is from the mean
np.std(a2)
# Standar deviation = Square Root of Variance
np.sqrt(np.var(a2))

Variance

  • The average of the squared differences from the Mean.
# Varainace = measure of the average degree to which each number is different to the mean
# Higher variance = wider range of numbers
# Lower variance = lower range of numbers
np.var(a2)

Example:

image

  • The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm
  • Mean = (600 + 470 + 170 + 430 + 300)/5 = 394mm

image

  • Variance = 21704
  • Standard Deviation = sqrt(variance) = 147 mm

Screenshot 2021-03-19 at 10 51 56 PM

  • we can show which heights are within one Standard Deviation (147mm) of the Mean:
  • Standard Deviation we have a "standard" way of knowing what is normal, and what is extra large or extra small

image