What is the difference between discrete data and continuous data?

  • What is the difference between discrete data and continuous data?

    Did you try Google first? For me, it gives http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Disc_Cont.htm" target="_blank">this.

    Here is a nice video which answers your question. https://www.youtube.com/watch?v=MIX3ZpzEOdM

    Just think digital vs analog. Same thing - different names.

    I truly don't know what the difference between "discrete" and "continuous" data. For some reasons, intro stat classes seem to really enjoy making students memorize rules to distinguish these two things. As far as I've been able to understand, the differences are not in the data--but in how we choose to model the data.

    This was the top result in Google, @robingirard.

    All actual and physically existing data, be it stored in writing, on tape, disk or in the brain is discrete both in space and in time at least as long as we hold QFT more fundamental than Newton, which means that continuous data doesn't really exists, but it can be derived from discrete data.

  • walkytalky

    walkytalky Correct answer

    10 years ago

    Discrete data can only take particular values. There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between. Discrete data can be numeric -- like numbers of apples -- but it can also be categorical -- like red or blue, or male or female, or good or bad.

    Continuous data are not restricted to defined separate values, but can occupy any value over a continuous range. Between any two continuous data values, there may be an infinite number of others. Continuous data are always essentially numeric.

    It sometimes makes sense to treat discrete data as continuous and the other way around:

    • For example, something like height is continuous, but often we don't really care too much about tiny differences and instead group heights into a number of discrete bins -- i.e. only measuring centimetres --.

    • Conversely, if we're counting large amounts of some discrete entity
      -- i.e. grains of rice, or termites, or pennies in the economy -- we may choose not to think of 2,000,006 and 2,000,008 as crucially
      different values but instead as nearby points on an approximate
      continuum.

    It can also sometimes be useful to treat numeric data as categorical, eg: underweight, normal, obese. This is usually just another kind of binning.

    It seldom makes sense to consider categorical data as continuous.

    @walktalky as @jeromy alludes to, in psychology at least, categorial variables such as reponses to questions are often presumed as being a representation of a underlying trait, so in that sense categorial data is sometimes taken as being continuous.

    @richiemorrisroe One could nitpick about the difference between the data and the putative trait, but of course you are right. Some very interesting further points were made in response to this follow-up question.

    thanks for the link, those answers are indeed very interesting.

    > "*There may potentially be an infinite number of those values, but each is distinct and there's no grey area in between*" -- it's actually perfectly possible to have a discrete distribution with distinct values, and *yet at the same time*, for any two distinct values you pick, always have more values between them ('grey area' in a sense). They don't come up all that often in practice, but it's perfectly possible for them to come up for real; indeed I can think of two distinct (if related) examples that can easily arise.

    so to clarify, even if you had 10 billion rows of ohlc data for a stock asset, it would be still be considered discrete? but then cant the price of an asset be anything between 1 to infinity, how to think in this type of situation?

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