# The Normal Distribution

**Episode #6 of the course “Equations that changed the world”**

The mathematical field of probability collects data in order to make predictions about unknown variables, so the more data included in a data set, the more accurate the predictions will be. When the collected information is plotted on a histogram, or bar graph, it may form a pattern where the two extreme ends of the data set show lower incidents of the variable being measured, and the majority of the incidents of the variable occurs toward the graph’s center. The bar graph may resemble a set of stairs that ascends along the x-axis, then descends from the center to the end of the data set.

This pattern is called a “normal distribution” of the data, because the variable of interest is most common around the data’s mathematical average, or “mean.” These graphs are also often referred to as “bell curves,” because if a curve is drawn over the tops of the bars in the graph, it resembles the shape of a bell. In a normal distribution, the data’s mean should be approximately equal to its median, with half of the data in the set falling below the median and half above it.

Normal distributions, or bell curves, can be calculated for many types of data sets. For example, in any group of people there will be a tallest person and a shortest person. Those two people’s heights serve as the extreme points on the distribution. The height of all group members could be used to calculate an average height. It is most likely that more people in the group will be close to the average height than will be close to either of the two extremes. When graphed, this data set would likely take the shape of a bell curve. Normal distributions are widely used across social and behavioral sciences, as well as in chemistry, physics, and economics.

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