"Degrees of Freedom (df)"

In the space of data analysis using statistics we often come across a term "degrees of freedom" (short form df). I will try to explain the concept in a intuitive way.

Let's say we are working on a sample of 7 (n) data points and there summation is 100, so by standard definition the degrees of freedom is always (n-1). So in our case it is 6. Let's try to understand why 6 and not 4 or 5.

We start putting in the numbers in a table as shown below. First number being 20 Second number being 12 and so on.

By the time you are on seventh number you will realise , in order to satisfy the condition of summation of all numbers should be equal to 100, the seven't number has to be 6 (the seventh number (last number) in sample cannot vary (it cannot take any other value than 6)).

As seen above numbers from 1 to 6 can take any value, but in order to satisfy the condition the seventh number cannot vary and has to take a fixed value to satisfy the summation condition. Hence degrees of freedom in above case is 6.