Difficulty: Introductory | Prerequisites: None
Before you can do anything useful in statistics, you need to know what kind of data you are looking at. The entire discipline branches differently depending on whether your data are numbers or categories, and whether those numbers can take any value on a line or only whole counts. This topic is the first thing covered in virtually every introductory statistics course because every method you learn later (choosing a graph, picking a test, interpreting output) depends on getting the data type right.
If you have not seen these terms before, start here. If you have, this is a quick refresher before moving into sampling and experimental design.
Data come in two broad flavours: qualitative (categories, labels) and quantitative (numbers you can do arithmetic on). Quantitative data split further into discrete (countable, whole numbers) and continuous (measurable, any value in a range). Categorical data split into nominal (no natural order) and ordinal (a meaningful ranking).
Qualitative data (categorical data)
Data that describe a quality or category rather than a numerical quantity. Values are labels or names.
Think of it as: the "what kind" column, not the "how much" column. Colour, make of car, shape of a container.
Quantitative data (numerical data)
Data that represent counts or measurements and on which arithmetic operations make sense.
In simple terms, if you can meaningfully add or average the values, they are quantitative. Mass in grams, speed in m/s, number of objects.
Discrete data
Quantitative data that can take only isolated values, typically whole numbers from counting.
Think of it as: things you count one by one. Number of crew members, number of species, a ranking position.
Continuous data
Quantitative data that can take any value within an interval, including fractions and decimals.
In simple terms, these come from measuring rather than counting. Height, weight, time remaining, average height.
Nominal data
Categorical data with no natural or meaningful order. The categories are just labels.
Think of it as: you could rearrange the list and nothing would be lost. Pizza toppings, names of friends, favourite days of the week listed without ranking.
Ordinal data
Categorical data where the categories have a meaningful order or ranking, but the distances between ranks are not necessarily equal.
In simple terms, first, second, third matter, but the gap between first and second is not guaranteed to be the same as between second and third. Race results (won, placed, showed), size categories (small, medium, large, jumbo).
Every piece of data is either qualitative or quantitative. Ask: "Can I do arithmetic on this value and have it mean something?"
Qualitative examples: the make of a car (Ford, Toyota), a license plate number (VNS-862), the colour of a chemical sample, the name of a material, the shape of a container.
Quantitative examples: the mass of a chemical sample, the length of an object in feet, speed in metres per second, the number of objects that are blue.
A license plate number looks numerical but is qualitative. You would never average two license plates. The digits are labels, not measurements.
Discrete data arise from counting. There are gaps between possible values (you cannot have 3.7 crew members).
Number of crew members on a boat
Pre-season ranking of a basketball team
Number of species of trees in a park
A dice total (2 through 12, whole numbers only)
Continuous data arise from measuring. Between any two values, another value is possible.
Average height of players on a team
Speed of a boat's propeller in revolutions per minute
Time remaining for a music download
Latitude and longitude of a location
Rule of thumb: if the value answers "how many," it is likely discrete. If it answers "how much" or "how long," it is likely continuous.
Nominal data are categories with no inherent order.
Pizza toppings (pepperoni, olives, mushrooms): rearranging the list changes nothing.
Favourite days of the week listed without ranking.
Names of friends listed with no preference order.
Ordinal data are categories with a meaningful sequence.
Race results: won, placed, showed. The order matters.
Pizza sizes: small, medium, large, jumbo. There is a clear progression.
"My favourite day is Friday, second-favourite is Saturday" introduces a rank, making it ordinal.
Key distinction: if the statement "i. My favourite days are Friday, Saturday, and Tuesday" (no ranking implied) is nominal, but "ii. My favourite day is Friday, second-favourite Saturday, third-favourite Tuesday" is ordinal because it ranks them.
Students often think a license plate number is quantitative because it contains digits. It is not. If averaging the value would be meaningless, it is qualitative.
Students confuse "discrete" with "qualitative." Discrete data are still quantitative (they are numbers you count). The word "discrete" describes how the numbers behave, not whether they are numbers.
Students assume ordinal data must be numbers. Ordinal data can be words (small, medium, large) as long as the words have a natural order.
Students mix up nominal and ordinal by focusing on the content rather than whether a ranking is stated. A list of days is nominal; the same days ranked by preference are ordinal.
⚠️ Expect questions that give you a specific real-world measurement and ask you to classify it. Read carefully: "the number of vehicles" is discrete, but "the average height" is continuous.
⚠️ License plate numbers and similar identifiers are a favourite trick question. They look numerical but are qualitative.
⚠️ The nominal vs ordinal distinction often hinges on a single word. "My favourite days are..." (nominal) vs "My favourite day is X, second-favourite is Y" (ordinal). Watch for ranking language.
⚠️ Dice totals are quantitative and discrete, not qualitative. The total is a number you can add and average, and it takes only whole values.
True or false: The number of trees in a park is continuous data. (False, it is discrete.)
Fill in the blank: Data that describe a quality or category rather than a number are called ______ data. (Qualitative.)
True or false: Pizza sizes (small, medium, large, jumbo) are an example of nominal data. (False, they are ordinal because the sizes have a natural order.)
Fill in the blank: If a value answers "how many," it is likely ______. (Discrete.)
True or false: A license plate number such as VNS-862 is quantitative data. (False, it is qualitative.)
Q: The make of a car with license plate VNS-862 is what type of data?
A: Qualitative. "Make" is a category (Ford, Honda, etc.), not a number.
Q: Which of the following is discrete: (a) average height of players, (b) pre-season ranking, (c) speed of a propeller?
A: (b) Pre-season ranking. It is a whole number from counting position. The other two are continuous because they come from measurement or averaging.
Q: A horse race result where Betty's Girl won, Mr. Ed placed, and Wabash showed. Is this ordinal or nominal?
A: Ordinal. The finishing positions (won, placed, showed) have a meaningful order.
Q: When rolling two six-sided dice, the total ranges from 2 to 12. Is this quantitative and discrete, or quantitative and continuous?
A: Quantitative and discrete. The total is a number (quantitative) that can only take whole values from 2 to 12 (discrete).
Q: Michaelangelo's sells small, medium, large, and jumbo pizzas. Is this nominal or ordinal?
A: Ordinal. The sizes have a natural progression from smallest to largest.
Q: Michaelangelo's most-requested toppings are pepperoni, olives, and mushrooms. Is this nominal or ordinal?
A: Nominal. The toppings are categories with no inherent ranking.
This connects to sampling methods because the type of data you collect determines which sampling and analysis techniques are appropriate. Categorical data often call for frequency tables and bar charts, while continuous data call for histograms and measures like the mean and standard deviation.
This also connects to experimental design: when you define your outcome variable, you must know whether it is qualitative or quantitative, discrete or continuous, to choose the right statistical test later in the course.
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