/dsc-distributions-recap-v2-2

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Statistical Distributions - Recap

Introduction

You have now completed the second of two foundational statistics sections! In the following section you will apply this knowledge of statistical distributions to begin finding inferential statistics.

This short lesson summarizes the topics we covered in this section.

Key Takeaways

In this section, we dug into statistical distributions.

Key takeaways include:

  • There are two ways we categorize distributions: discrete and continuous

    • Discrete distributions have a distinct, non-infinite number of possible values. For example, the number of bedrooms in a house is discrete. We describe discrete distributions using probability mass functions (PMFs).
    • Continuous distributions have effectively an infinite number of possible values (subject to measurement and/or storage precision). For example, a person's height is continuous. We describe continuous distributions using probability density functions (PDFs) and cumulative distribution functions (CDFs).

  • Highlighting some specific distributions:

    • Bernoulli Trials deal with a series of boolean events, which is a type of discrete distribution
    • The normal distribution is the classic "bell curve" with 68% of the probability mass within 1 SD (standard deviation) of the mean, 95% within 2 SDs, and 99.7% within 3 SDs.
      • The standard normal distribution is a standardized version of the normal distribution, where the mean is 0 and the SD is 1

  • Insights regarding distributions:

    • The z-score can be used to understand how extreme a certain result is
    • Skewness and kurtosis can be used to measure how different a given distribution is from a normal distribution

    Appendix

    Recall that there is additional material in the Appendix for you to review if you have time. In particular:

    • The uniform distribution, which represents processes where each outcome is equally likely, like rolling dice
    • The Poisson distribution, which can be used to represent the likelihood of a given number of successes over a given time period
    • The exponential distribution, which can be used to represent the amount of time it may take before an event occurs