Degree of freedom

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    I’m having a hard time putting this question in simple term so i can understand. Maybe somebody can assist me. “Degree of Freedom is usually n-1; why?”



    Does this answer your question?


    Arun Bhat

    The no of values you are free to select is known as the degrees of freedom (DOF)
    I will try to explain you with an example, if your are told to decide 6 numbers  such that the average of those  is 10. Here will realize that you are free to select only 5 of the 6 numbers , you will not have control over the  6th number it is  fixed.
    20,10 8,5, 15 are the 5 numbers that you have taken, the 6th number should be “2” than only your condition (average=10) will satisfy.
    So out of 6 choices actually you have only 5 choices
    this is nothing but (n-1)
    I hope this clears your doubt



    Degrees of freedom is the term used to eliminate bias in your data.
    Bias is the term used when you can foretell the data(number) you want to collect.
    to illustrate:
    If you have four golf balls numbered with 1, 2, 3, and 4 in a basket. One of these balls will be randomly taken out ( n-1 ) and you will be left with three balls to pick in the basket. You don’t know what number was taken out so, you cannot tell what are the three numbers left.
    1. Before you pick the first ball, can you tell me the number  you will get? Of course not because numbers 1, 2, 3, and 4 have the same probability of being picked. 1/4 ( ohh! it’s number 3, keep the number 3 ball )
    2. before you pick the second ball, can you tell me the number you will get? Again, you can’t because numbers 1, 2, and 4 have the same probability to be picked. 1/3 ( ohh! I got number 1, keep the number 1 ball )
    So, you already have number 1 and 3 and there’s only one ball in the basket, can you tell me what number is that remaining ball? Nope, you can’t because of ( n-1 ). the remaining ball can be 2 or 4 with the same probability to be picked- 1/2.
    hope this helps.

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