Standard Normal Distribution

• Standardization:
  • Every distribution can be standardized.
• When we standardize the normal distribution, the result is Standard Normal distribution.
• Lets understand standardization with an example Refer Here for the example done in the class
• 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

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.
• Theorem can be Represented as
  • No matter the distribution
  • 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
  • Standard error is used in most statistical test because it shows how well you approximated the true mean