Data Science Classroom Series – 03/Nov/2021

Standard Normal Distribution

  • Standardization:
    • Every distribution can be standardized. Preview Preview
  • When we standardize the normal distribution, the result is Standard Normal distribution. Preview
  • Lets understand standardization with an example Refer Here for the example done in the class Preview
  • Why Standardize:
    • Standarization allows us to:
      • Compare different normally distributed datasets
      • detect normality
      • detect outliers
      • create confidence intervals
      • test hypotheses
      • perform regression analysis
  • Exercise: Try to standardize the following approximate normal distribution Refer Here Preview

The Central Limit Theorem (CLT)

  • The CLT is one of the greatest statistical insights.
  • It states no matter what the underlying distribution of the dataset, the sampling distribution of the means would approximate to normal distribution.
  • Moreover, the mean of the sampling distribution would be equal to mean of the original distribution & variance would be n times smaller. where n is size of the sample. Preview
  • Theorem can be Represented as
    • No matter the distribution Preview
    • The more samples, closer to the Normal.
  • Standard Error: The standard deviation of the distribution formed by the sample means. Standard Error represents the variability of sample means Preview
    • Standard error is used in most statistical test because it shows how well you approximated the true mean

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