The Main Ideas behind Probability Distributions

Stat Quest, Stat Quest, Stat Quest, Stat Quest, StatQuest! Hello, and welcome to StatQuest! StatQuest is brought to you by the friendly folks in the genetics department at the University of North Carolina at Chapel Hill Today, we're going to be talking about what a distribution is. Imagine you're at a wild and crazy dance party and you overhear someone talking about statistics.

Chances are, they're going to be talking about distributions... Dag! What is a statistical distribution? Imagine we measured the height of a lot of people The first person we measured was 5.2 feet tall So we put that measurement in a bin that spans from 5 feet to 5.5 feet The second person we measured was 5.8 feet tall

The third person we measured was 5.6 feet tall The fourth person we measured was 5.9. feet tall The fifth person we measured was only 5.1 feet tall And the sixth person we measured was 6.3 feet tall OK, you get the idea - we measure a bunch of people and put the measurements in bins.

When you stack a bunch of measurements into bins like this, you get a histogram Most of the measurements come from people between 5 and 6 feet tall People smaller than 5 feet tall were relatively rare People taller than 6 feet tall were also relatively rare In other words, if you picked one measurement at random, there's a good chance it would be between 5 and

6 feet tall The histogram gives us a sense of how likely we'll measure someone really tall or really short or closer to the average What if we use smaller bin sizes for our measurements? Now the bins are half as wide as before And here's how our data stacks up in the smaller bins