Modeling data distributions

This course is a part of Statistics and probability, a 16-course Topic series from Khan Academy.

This unit takes our understanding of distributions to the next level. We'll measure the position of data within a distribution using percentiles and z-scores, we'll learn what happens when we transform data, we'll study how to model distributions with density curves, and we'll look at one of the most important families of distributions called Normal distributions.

This course contains 7 segments:

Percentiles

Let's learn about percentiles, which measure what percent of data is at or below a given point in a distribution.

Z-scores

We use standardized scores (also called z-scores) to measure position in a distribution by looking at exactly how many standard deviations away from the mean a given data point is.

Effects of linear transformations

We can predict how transforming a set of data will impact measures of center and spread.

Density curves

A density curve models the distribution of a quantitative variable with a smooth curve. The area under a density curve over some interval represents what proportion of observations fall in that interval. Let's learn how to create density curves and understand their properties.

Normal distributions and the empirical rule

Here we introduce perhaps the most important type of distribution in statistics — the normal distribution. We'll look at what exactly makes a density curve "normal," and we'll learn about the empirical rule (also called the 68-95-99.7 rule).

Normal distribution calculations

We use z-scores to solve problems involving area under a normal distribution.

More on normal distributions

What exactly do we mean when we say a variable is normally distributed? Let's look at some mathematical properties of normal distributions.