Probability and Statistics > Statistics Definitions > Location Parameter

## What is a Location Parameter?

The location parameter tells you where your graph is located. More specifically, it tells you **where on the horizontal axis a graph is centered, relative to the standard normal model.** The standard normal distribution curve is centered at 0 (the mean), so a parameter of 5 lets you know a graph is centered 5 units to the right of the curve’s center, at x = 5.

The normal distribution curve on the **left** has a location parameter of 0 and on the right, it’s 10.

A location parameter of -10 moves the graph 5 units to the *left* of zero, at x = -5.

### Relationship to translations in geometry

Location parameters are similar the concept of **translations** in geometry, where a shape is moved in a certain direction depending on the translation. However, in geometry an object can be translated by angle and distance or by x and y. In statistics, the type of translation defined by the location parameter is only a **translation on the x-axis**.

### Notation

A location family is a set of probability distributions where μ is the location parameter. For example, μ = 9 tells you the center of the graph is located at x = 10.

### Mean and Standard Deviation

For the normal distribution, the location parameter is the mean of the data set. However, this is **not true** for most other distributions.

## Location Family

A location family is a class of probability distributions where x_{0} determines the location of the distribution. Probability density functions or probability mass functions in the **location family** are defined by the following equation:

F_{x0}(x) = f(x – x_{0}) where x_{0} is the location parameter.

If x_{0} is **increased**, the graph of the probability function moves to the right on the horizontal axis and if x_{0} is **decreased**, the graph moves to the left on the horizontal axis.

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