# Restriction of Range: Definition & Examples

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• 0:01 What Is Restriction of Range?
• 1:14 The Correlation Coefficient
• 2:45 Why Restricting the…
• 3:21 Lesson Summary

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Lesson Transcript
Instructor: David Karsner
In this lesson, we'll use real-life examples and charts to learn about restriction of range, a statistical technique in which only part of the data available is used to find the connection between two variables or quantities.

## What Is Restriction of Range?

Just for a minute, imagine that you're a school administrator looking to find the grade point average (GPA) of the Class of 2015 at Central High School in Somewhere, U.S.A. However, instead of calculating the mean (or average) GPA of the entire graduating class, you calculated the mean GPA for the 25 students in the senior English honors class.

In this scenario, you've restricted the range. In the field of statistics, restricting the range means to limit the data in the population to some criterion, or use a subset of data to determine whether two pieces of information are correlated, or connected. Let's look at another example. Let's say you're interested in the exercise habits of young adult Americans but only poll college students with an athletic scholarship.

In both examples, you used data from a sample population whose results would differ from those found in the general population. As such, your results will not satisfy the original inquiry: students in an English Honor class will most likely have higher grades than the average of the entire student body, while college students on athletic scholarships will most likely spend more time exercising.

## The Correlation Coefficient

When you plot a set of data on an xy grid, the correlation coefficient is a number between -1 and 1 that tells you how likely the data is to form a line, or have a linear relationship. A set of data with a correlation coefficient of zero means the two variables do not share a linear relationship. However, the correlation gets stronger as the coefficient gets closer to 1 and -1, which means the data forms a line. When you restrict the range of a data set, it causes the correlation coefficient to move toward zero.

This chart shows how 21 students did on a test in relation to how many minutes they spent studying.

If you enter the data set into a graphing calculator and ask it to run a linear regression, or relationship model, with a correlation coefficient, your result will be .746. According to the results, test scores and time studying are linearly correlated. In everyday language, the more time the 21 students spent studying, the higher they scored on the test.

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