# Discrete or Continuous Variables

I am having a hard time determining if these are either discrete or continuous.

The number of visits to a website in a particular week.

• I said this was discrete because it is finite.

The height of the ocean’s tide at a given location.

• I said this was continuous because it is not always finite.

The time to complete a questionnaire.

• I said this was continuous because it is not always finite.

The number of consumers in a poll of 1000 who agree with the poll question.

• I said this was continuous because it is not always finite.

The rainfall total for a city in a year.

• I said this was continuous because this is not always finite.

The number of heads occurring in 3 tosses of a single coin.

• I said this was discrete because it is a finite.

I am not 100% sure of my answers.

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I, personally, always take issue with these sorts of questions--the idea that the height of an ocean's tide being continuous ignores that the world is made of discrete particles (atoms)... (at least, IMO.) – apnorton Feb 15 '14 at 21:12

## 2 Answers

Discrete does not mean nor imply finite: it means that there is a minimum "gap" between the values the variable can take.

E.g.:

• The number of visits to a website in a particular week.
• must be an integer, so two values are always separated by at least 1: it is discrete.
• The height of the ocean’s tide at a given location.
• as a first approximation, it can take absolutely any value within a range, say $[0, 10^6]$: there is no "granularity" here (if you give two possible values $a$ and $b$, $\frac{a+b}{2}$ is also a possible value).
• The number of consumers in a poll of 1000 who agree with the poll question.
• it is again an integer: discrete. You cannot have $2.46477655\dots{}$ people agreeing.
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As a further remark: continuous implies infinite by definition. So if your variable can only take a finite number of values, it has to be discrete. – Clement C. Feb 15 '14 at 21:00

Most of your answers are right. However, I think you have a slightly wrong idea of what's the difference between discrete and continuous.

A nice way to think of it is: if given one value, you exactly what comes next (its successor), then the value is discrete.

For instance, if we're counting people and we have 15 people, we know the next number is $16$ people. However, if I'm $175$cm tall and we're allowed to be very precise, what comes next? $176$? $175.1$? $175.000001$?

If you're pooling $1000$ people, then definitely there cannot be for instance $45.0001$ voters, so the variable is discrete.

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