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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Z-Score Tutorial

Characteristics of a Normal Distribution

a bell-shaped curve marked with the mean in the middle and incremental lines marking standard deviations away from the central mean


Characteristics of a Normal Distribution:

Normal distributions are not all exactly the same size or shape. However, they all possess the same key features:

  • mean = median = mode - located in the middle of the distribution
    • so half of the distribution (50%) lies above the mean and half of the distribution lies below the mean
  • symmetrical distribution about the mean
    • if you folded the distribution in half along the mean, the halves are mirror images of each other


The Standard Normal Distribution:

The Standard Normal Distribution is a special case of the normal distribution that takes on a specific shape with a given mean and standard deviation:

  • mean = 0
  • standard deviation = 1

We also refer to the Standard Normal Distribution as the Z-Distribution because we often speak about this distribution in terms of z-scores, which you can learn more about on the next tab.