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- Thread starter Mr Davis 97
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So a variable in descriptive statistics is pretty logical: it is some quantity that has been measured and that we have certain measurements for. Random variables are a lot harder since the measurement has not yet been made. Again, random variables are certain quantities. But now we must prepare ourselves for all possible outcomes of the experiment! So a random variable measures all possible outcomes of a measurement and the probability distribution gives the probabilities for these outcomes. The idea is that we then do an experiment and get certain outcomes. These outcomes can be described with descriptive statistics and we hope that the distribution (in the descriptive sense) agrees with the probability distribution.

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Okay, I see. So would it be correct to say something along the lines of: Inferential statistics uses random variables and their associated probability distributions in order to theoretically idealize a certain experiment in terms of outcomes and the distribution of those outcomes? Also, another question: why do we only describe a the distribution of a random variable with a probability distribution? Why are there not other ways that are analogous to descriptive statistics, such as a frequency table?

So a variable in descriptive statistics is pretty logical: it is some quantity that has been measured and that we have certain measurements for. Random variables are a lot harder since the measurement has not yet been made. Again, random variables are certain quantities. But now we must prepare ourselves for all possible outcomes of the experiment! So a random variable measures all possible outcomes of a measurement and the probability distribution gives the probabilities for these outcomes. The idea is that we then do an experiment and get certain outcomes. These outcomes can be described with descriptive statistics and we hope that the distribution (in the descriptive sense) agrees with the probability distribution.

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