Online Mathematics Book

Types of Data

We now learn about the different types of data we'll come across in statistics.

Before learning any methods for calculations and illustrations in statistics, it is essential to know how to distinguish the different types of data we may need to analyze.
That is what we learn in this section.

To begin with, we start by watching the tutorial, below.
Do take the time to watch this as they will help in understanding.

Tutorial: Types of Data

Following the tutorial we just watched, we define the different types of data.

Qualitative Data

Qualitative data is characterized by some quality, or its belonging to some category.

The main type of statistical analysis we do with this type of data is done with graphical methods, such as bar charts, pie charts, pictograms.


Some examples of scenarios in which we'd be observing qualitative data are listed here:

  • A group of people asked which color t-shirt they prefer, between blue, pink, green and red.
    The data collected would be a list, or a tally chart of colors blue, pink, green and red. That is qualitative data.
  • Asking all middle and high school students which additional language they are learning in school.
  • \(100\) people being asked which device to study with, between, computer, smartphone or tablet.
  • A survey conducted to determine which smartphone brand people prefer: Apple, Samsung, Google, LG, Sony.

Quantitative Data

Quantitative data comes in one of two categories. Those are discrete data and continuous data.

Discrete Data

Discrete data can only take-on certain values, or certain types of values.
Given two distinct observations of discrete data it is not possible for another observation to take-on any value between them (only certain values).
For example, when buying a pair of shoes, we can buy a size \(7\) or a size \(8\). We may also be able to buy a size \(7.5\). But we cannot by a size \(7.326573\), that number is not a possible shoe size in stores.
Shoe sizes correspond to discrete data.


Discrete Data

The following is a list of scenarious in which the data collected would be discrete quantitative data:

  • Number of pages in a book.
  • Number of rooms in a hotel.
  • Grade obtained at a multiple choice test.
  • Number of turns it takes for a chess player to win.

Continuous Data

Continuous data is characterized by the fact that it can take-on any value between any two distinct observations.
Some typical examples of continuous data would be length and time.
For example, the World Record for \(100\)m sprint is \(9.58\)s. This value is limited by the accuracy of the instruments with which time was measured. The actual time taken to run the \(100\)m could be anything between \(9.575\)s and \(9.585\)s.
The time may well be \(9.58143256378\)s.
Data such as this, which is limited by the accuracy of the instruments with which they are measured, are contnuous.


Continuous Data

The following is a list of scenarious in which the data collected would be continuous quantitative data:

  • Time it takes for an ice cube to melt.
  • Pressure in a tyre.
  • Time taken to run a \(10\)km race.
  • Length of a mouse's tail.

Continuous Data

Continuous data is measured. The actual value we use depends on the level of accuracy we need as well as the measuring accuracy of the tools used.

Discrete Data

Discrete data isn't measured. It is counted or read; we don't measure shoe sizes, we read them.

Exercise 1

State whether each of the following data types is qualitative of quantitative:

  1. hair color
  2. shoe size
  3. number of pages in books
  4. day of the week
  5. favorite device to study with: laptop, tablet, or smartphone
  6. length of one's foot
  7. number of messages sent with a smartphone in a day
  8. favorite brand of phone
  9. time taken to run \(100\)m
  10. people's heights

Answers Without Working

  1. qualitative
  2. quantitative
  3. quantitative
  4. qualitative
  5. qualitative
  6. quantitative
  7. quantitative
  8. qualitative
  9. quantitative
  10. quantitative

Exercise 2

State whether each of the following quantitative data types is discrete or continuous:

  1. Number of pets each student has.
  2. The weight of each student in a class.
  3. Number of teeth various mammals have.
  4. Temperature in different rooms of a school.
  5. Stopping distance of a car.
  6. Difference, in points won, between winner and loser at a game of table tennis.
  7. The weight gain, during a baby's first week among us.
  8. The heights of trees in a portion of a forest.
  9. Number of coffees one has in a day.
  10. Number of goals scored in a game of football.

Answers Without Working

  1. Discrete Data
  2. Continuous Data
  3. Discrete Data
  4. Continuous Data
  5. Continuous Data
  6. Discrete Data
  7. Continuous Data
  8. Continuous Data
  9. Discrete Data
  10. Discrete Data