Probability and statistics
Practice this topic
Descriptive statistics
Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation.
Measures of central tendency
This is the foundational tutorial for the rest of statistics. We start thinking about how you can represent a set of numbers with one number that somehow represents the "center". We then talk about the differences between populations, samples, parameters and statistics.
Box-and-whisker plots
Whether you're looking at scientific data or stock price charts, box-and-whisker plots can show up in your life. This tutorial covers what they are, how to read them and how to construct them. We'd consider this tutorial very optional, but it is a good application of dealing with medians and ranges.
Variance and standard deviation
We have tools (like the arithmetic mean) to measure central tendency and are now curious about representing how much the data in a set varies from that central tendency. In this tutorial we introduce the variance and standard deviation (which is just the square root of the variance) as two commonly used tools for doing this.
- Variance of a population
- Sample variance
- Review and intuition why we divide by n-1 for the unbiased sample variance
- Simulation showing bias in sample variance
- Unbiased Estimate of Population Variance
- Another simulation giving evidence that (n-1) gives us an unbiased estimate of variance
- Simulation providing evidence that (n-1) gives us unbiased estimate
- Will it converge towards -1?
- Variance
- Statistics: Standard Deviation
- Exploring Standard Deviation 1 Module
- Exploring standard deviation 1
- Standard deviation
- Statistics: Alternate Variance Formulas
Sal's old statistics videos
This tutorial covers central tendency and dispersion. It is redundant with the other tutorials on this topic, but it has the benefit of messy handwriting and a cheap microphone. This is Sal circa 2007 so take it all with a grain of salt (or just skip it altogether).