Data is observation. A random variable is a variable that can contain several values based on stochastic process.
Data will represent the randomness in the variables. unless a specific random variable has effect on the process, it will no longer be considered (randomness).
hope I have addressed your query.
Data. values are usually often be a real collection by viewing
Random variable. Values are produced randomly or set of possible values of the random experiment
Random variable can assume a value out of all possible data. The quantitative or qualitative description of the variable for the event may termed as data.
Fausto, replace "description" by "realization" in Rajivs answer. I think then it makes some sense: Data are realizations of a random variable. And, as you noted, a random variable is defined by its probability distribution.
The question is certainly important. I would add to Rajiv, Jochen and Fausto these points: 1) In the population of interest we need several, N, individual cases to measure some variable of "research interest" they portray (individual case datum); the series of those N measured and registered values conform the "dataset". 2) In this process, we need a method that fits some criterion to select those cases, like being "representative" of the wider population of interest, so we design "random processes" of sampling that ideally guarantee that they fit the goals we seek, and that "dataset" obtained is useful for next step of analysis. If so, we call this entity a "random variable", and this means that we joined the mathematical term "variable" to the "random" selection process. 3) In the step of analysis we order the variable and study its relation as a function of population frequences (that may come as elementary ones, or as cummulative-ordered ones) using different methods, approaches, logics and models.
Even if dataset, or "data", is not a "random variable", we may analyze it assuming it is only representative of itself, but not of a wider set.
I add all this only to say that "random variables" have this sense inside the activity of sampling for research purposes and statistical analysis. Thanks, emilio
Say, we have measure the blood pressure of 10 people over 40 years of age. Value of BP of each people is data, but if we say before measuring the BP that those who are above 140/90 mm of Hg is hypertensive, and below 140/90 mm of Hg is normotensive then our variable is “hypertensive” and “normotensive”
So if we record the BP in a chart that will be like this
Sl No
BP
Hypertensive / Normotensive
1
120/80
Normotensive
2
150/95
Hypertensive
3
110/75
Normotensive
4
135/85
Normotensive
5
130/85
Normotensive
6
125/80
Normotensive
7
160/100
Hypertensive
8
135/90
Normotensive
9
115/70
Normotensive
10
180/95
Hypertensive
From the above table we can say that among the 10 persons 3 are suffering from hypertension
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