# what are degrees of freedom in statistical mathematics. explain in layman's words?

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The degrees of freedom are the number of extra numbers you need to specify your data completely, after you have provided a summary of your data.

Example: You have ten numbers. You also know that the mean is 1.3 and the standard deviation is 0.6. Since ten numbers were required to describe your data completely and you already have two, the degrees of freedom are 10-2=8.

This is an important concept when doing statistical tests. For example, suppose you have a 2x2-table and you want to apply the chi-square test for independence between rows and columns. The chi-square test is based on the assumption that you already know 3 numbers: the row proportions, the column proportions and the totalt number of observations. Since the total number of number in your table is 4, and 3 were already known before you started to compute the chi-square statistic, the degrees of freedom is 4-3=1. Now the theory says that you must use the chi-quare table with one degree of freedom.

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• Anonymous
4 years ago

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• The "degrees of freedom" are the independent pieces of information needed to exactly specify the state of a system. For instance, a particle moving in three dimensional space has 6 degrees of freedom.

Three numbers are needed to describe the position of the particle in space. (The x, y, and z coordinates do nicely.) Another three numbers are required to specify the velocity of the particle. (The components of the velocity vector in the x, y, and z directions for instance.) Thus, we need 6 numbers to exactly describe the particle's state.

There are many other situations where we can talk about "degrees of freedom". For instance, we may be studying the relationship between age, sex, and college GPA in a population. In this situation, we have three "degrees of freedom" for each person.

Source(s): My math PhD
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Stats tries to predict a number out of past data. For example, if we think the number is 10, 'Give or Take' 4. The give or take part is the degree of freedom.

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• Degrees of freedom is used to minimize the error of the results in statistics. That is why it is called degrees of freedom.

Degrees of freedom: The maximum number of quantities whose values are free to vary before the remainder of the quantities are determined.

Hope this helps

Source(s): www.knowledgebank.irri.org/glossary/Glossary/D.htm
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