Percentiles and moments¶

Python notebook: https://github.com/daviskregers/data-science-recap/blob/main/04-percentiles-and-moments.ipynb

Percentiles¶

• In a data set, what's the point at which X^ of the values are less than that value?
• Example: income distribution
  • 99% percent of people make less than $506,553
  • 50% of people make less than $42,327

Moments¶

• Quantitative measures of the shape of a probability density function
• Mathematically they are a bit hard to wrap your head around:
  • $$ \mu n = \int^{+\infty}{-\infty}(x - c)^nf(x)dx $$ (for moment n around value c)
• But intuitively, it's a lot simpler in statistics

• The first moment is the mean.
• Second moment is the variance
• Third moment is is "skew" (\(\gamma\))
  • How "lopsided" is the distribution?
  • A distribution with a longer tail on the left will be skewed left, and have a negative skew.

• 4th m oment is "kurtosis"
  • How thick is the tail and how sharp is the peak, compared to a normal distribution?
  • Example: higher peaks have higher kurtosis