The Normal Distribution

Central Limit Theorem

  • randomly selected.
  • independent. Samples can’t influence each other.
  • large enough. 30 is usually considered enough for a normally distributed population, but no more than 10% of the whole population — if there are no replacements.

Characteristics of a Normal Distribution

  • The area under the curve is equal to 1.0.
  • They are denser in the centre and less dense in the tails.
  • Around 68% of the area of a normal distribution is within one standard deviation of the mean (μ - σ) to (μ - σ).
  • Approximately 95% of the area of a normal distribution is within two standard deviations of the mean (μ - 2σ) to (μ + 2σ).
  • Approximately 99.7% of the area of a normal distribution is within three standard deviations of the mean (μ - 3σ) to (μ + 3σ).
  • Values outside of 3σ tend to be considered extreme, with a very low probability of occurrence.

Skewness and Kurtosis

  • When negative the left tail is stretched.
  • When null, the distribution is symmetrical.
  • When positive, the right tail is stretched.
  • Platykurtic means the tails are going to be longer, thicker; as a result , the centre of the distribution will be less pronounced. The distribution appears flatter. (in Blue)
  • Mesokurtic means the distribution is what we’d expect from a Gaussian distribution. (in Red)
  • Leptokurtic means the tails are shorter, thinner; the centre of the distribution is denser. The distribution appears thinner. (in Green)





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Antoine Ghilissen

Antoine Ghilissen

Data Scientist

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