Here’s a table that summarizes the types of variables:

Types of variables |
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Quantitative(a.k.a. Numerical) |
Qualitative(a.k.a. Categorical) |
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Continuous |
Discrete |
Ordinal |
Nominal |

Consists of numerical values that can be measured but not counted. | Consists of numerical values that can be counted. | Consists of text or labels that have a logical order. | Consists of text or labels that have no logical order. |

e.g. Weight {56.06 Kg, 87 Kg} |
e.g. Number of disease cases {0, 1, 2, 3} |
e.g. Beverage size {small, medium, large} |
e.g. Profession {chemist, carpenter} |

There are 2 basic types of variables: quantitative and qualitative.

## 1. Quantitative or Numerical variable:

**A quantitative or Numerical variable is a type of variable consisting of values that represent counts or measurements of a certain quantity. **For instance, age, height, number of cigarettes smoked, etc.

A quantitative variable can be either continuous or discrete.

### 1.1. Continuous variable:

**A continuous variable is a type of quantitative variable consisting of numerical values that can be measured but not counted, because there are infinitely many values between 1 measurement and another.**

Example: Cholesterol level measured in mg/dl.

### 1.2. Discrete variable:

**A discrete variable is a type of quantitative variable consisting of numerical values that can be measured and counted, because these values are separate or distinct.** Unlike a continuous variable, if you select a value at random from a discrete variable, there is a concept of next and/or previous value.

Example: Vote count in an election.

A discrete variable may take on an infinite number of values as long as they are countable (even if we would be counting forever). For instance, the* “number of dice rolls until we get 2 consecutive sixes” *is a discrete variable because it is countable, although we could theoretically go on forever without getting 2 sixes in a row.

**⚠ Transforming text into discrete variables:**

Each unique word in a group of text documents can be transformed into a discrete numerical variable whose values are the number of occurrences of the word in each of the documents. This makes possible the statistical analysis of text from sources like: comments on social media, books, research articles, etc.

**In practice, all continuous variables are discrete!**

Since the precision of our measurements is not infinite, a theoretically continuous variable will practically be discrete i.e. it will only take on distinct values, although very close to one another.

However, for the purpose of analyzing data, we consider a variable continuous if it can take on a very large number of possible values within a certain interval such that it would be practically impossible for 2 observations to have the same value – in other words, within a given interval, the possible values that a continuous variable can take do not have to be literally infinite.

Here are some examples to help you differentiate between discrete and continuous variables:

### Exercise: Discrete or continuous?

#### – Is age discrete or continuous?

Age is a discrete variable when counted in years, for example when you ask someone about their age in a questionnaire. Age is a continuous variable when measured with high precision, for example when calculated from the exact date of birth.

#### – Is mass discrete or continuous?

Mass is a continuous variable since it can take on any value between its minimum and maximum. Mass is not discrete since there is no definite answer to the question: What is the next value for mass after, for example, 63.207 Kg?

#### – Is shoe size discrete or continuous?

Shoe size is a discrete variable since it takes on distinct values such as {5, 5.5, 6, 6.5, etc.}. Because there is a finite number of values between any 2 shoe sizes, we can answer the question: What is the next value for shoe size after, for example 5.5? The answer is 6 – making it a discrete variable.

#### – Is dosage of medicine discrete or continuous?

Dosage of medicine is a discrete variable if the medicine is administered as distinct doses of 5, 10, and 20 mg for example. Dosage of medicine is a continuous variable if the medicine is administered as a constant-rate intravenous infusion.

#### – Is systolic blood pressure discrete or continuous?

Theoretically, the systolic blood pressure of an individual is a continuous variable since it can take on any value between 0 and 300 mmHg. Practically, the systolic blood pressure as measured by a monitor is a discrete variable since it can only take on distinct values, such as: 140 mmHg, 141 mmHg, etc.

**⚠ Half continuous and half discrete variables:**

Some variables are continuous below a certain threshold and then become discrete as the accuracy of the measurements declines for larger values, such is the case with estimating of the time of death of a body. These are considered continuous variables, since it would be impossible to count all their individual values.

## 2. Qualitative or Categorical variable:

**A qualitative or categorical variable is a type of variable consisting of text characters or labels that describe groups of observations.** For instance, gender, marital status, stages of a disease, etc.

**⚠ Numbers representing categorical data:**

Sometimes categorical variables are coded as numbers instead of text, for instance:

- 0 and 1 to represent binary variables (e.g. Gender: where male is 0 and female is 1)
- ID numbers
- Passwords
- Phone numbers

A qualitative variable can be either ordinal or nominal.

### 2.1. Ordinal variable:

**An ordinal variable is a type of qualitative variable consisting of text or labels that have a logical order, i.e. one category represents more or less of the other, but taking the difference between categories or their average is meaningless.**

Example: Hypertension stages.

### 2.2. Nominal variable:

**A nominal variable is a type of qualitative variable consisting of text or labels that have no logical order.**

Example: Gender.

## Summary: A decision tree for identifying variable type

## References

- Triola M.
*Essentials of Statistics*. 6th edition. Pearson; 2018. - Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE.
*Regression Methods in Biostatistics: Linear, Logistic, Survival, and Repeated Measures Models*. 2nd edition. Springer; 2011. - Hastie T, Tibshirani R, Friedman J.
*The Elements of Statistical Learning: Data Mining, Inference, and Prediction*. 2nd edition. Springer; 2016.