### Chapter 1. Descriptive Statistics: Types of Data and Measurements

### Qualitative and Quantitative Variables

Before starting the analysis of a dataset, it is important to pay close attention to the type of data you are dealing with. Depending on the type of data, different statistical techniques should be used to describe and analyze the dataset. It is therefore essential to be able to correctly identify the type of data you are working with.

In statistics, there are two basic types of variables: *qualitative* and *quantitative *variables.

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Qualitative variable

**Definition**

A **qualitative** variable is non-numerical or categorical in nature, meaning names or labels are used to classify observations into different categories.

**Examples:**

- Color of the sky
- Texture of a shirt
- Favorite food
- Gender

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Due to its non-numeric nature, no mathematical operations should be applied to qualitative data. This drastically limits the number of statistical techniques that can be used to describe and analyze qualitative data.

One potential pitfall of dealing with qualitative data is that verbal labels (words/letters) are quite often *encoded* as numerical values. A common example is gender, which is often encoded using integers such that #\text{male} = 1#, #\text{female} = 2#, #3 = \text{other}# (or some other combination). It is important to note that, despite the use of numerical values to encode the data, no meaning should be attributed to these numbers. For example, it would be incorrect to state that because males are coded as #1# in the dataset and females as #2# females have twice as much gender as males.

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Quantitative variable

**Definition**

A **q****uantitative **variable is numerical in nature and is measured through acts of counting or with the use of measurement instruments.

**Examples:**

- The sum of two dice
- Number of students in a class
- Weight
- Length

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Quantitative variables can be further subdivided into two types: *discrete *and *continuous *variables.

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Discrete variable

**Definition**

A **discrete variable **can either take on a finite number of values or can take on infinitely many values that can be labeled with numbers (e.g. #0, 1, 2, 3\ldots#).

**Examples:**

- The sum of two dice
- Number of students in a class
- Number of siblings
- Amount of change in your pocket

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Continuous variable

**Definition**

A **continuous variable** can take on any value in one more or more intervals.

The precision with which one can express a continuous variable is dependent on the accuracy of the measurement instrument used to collect the data.

**Examples:**

- Weight
- Length
- Time
- Temperature

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