Quantitative Data Examples: Discrete, Continuous, Interval, Ratio

What is quantitative data? Definition and examples

Quantitative data are numbers that come from counting or measuring an attribute of a population. OpenStax’s Introductory Statistics 2e puts it flatly: “Quantitative data are always numbers.” Its examples are the amount of money, pulse rate, weight, and the number of people living in your town. Data that are the result of categorizing or describing attributes, such as hair color, blood type or the car someone drives, are qualitative instead (OpenStax, section 1.2). See qualitative data for that side, and categorical variable examples for the category-based variable types.

Two questions place any quantitative example: was it counted or measured (discrete or continuous), and does its scale support differences only or ratios too (interval or ratio)? The table below answers both for examples taken from OpenStax.

Quantitative data examples: counted or measured, and on what scale

Example	Counted or measured	Type	Scale	Basis
Number of daily phone calls (0, 1, 2, 3…)	Counted	Discrete	Ratio (zero calls means none)	Type: OpenStax 1.2. Scale: classified here by the minimum-value rule.
Number of people living in your town	Counted	Discrete	Ratio (zero means none)	Type: OpenStax 1.2. Scale: classified here by the minimum-value rule.
Length of phone calls in minutes (2.4, 7.5, 11.0)	Measured	Continuous	Ratio (zero minutes means no time)	Type: OpenStax 1.2. Scale: classified here by the minimum-value rule.
Weight	Measured	Continuous	Ratio (zero means no weight)	Type: OpenStax 1.2. Scale: classified here by the minimum-value rule.
Temperature in Celsius or Fahrenheit	Measured	Continuous	Interval	OpenStax 1.3 names both as interval scales.
Exam scores (80, 68, 20, 92)	Counted points	Discrete in this example	Ratio	Scale: OpenStax 1.3. Type: classified here by the counted-versus-measured rule.

Cells marked “classified here” apply OpenStax’s counted-versus-measured rule and its minimum-value rule to a plainly counted or measured quantity; the textbook does not label those cells itself.

Discrete vs continuous quantitative data

Discrete data are counted

“All data that are the result of counting are called quantitative discrete data” (OpenStax 1.2). The number of phone calls someone makes in a day can be 0, 1, 2 or 3, but never 2.4.

Continuous data are measured

Continuous data can be fractions or decimals and “are often the results of measurements like lengths, weights, or times” (OpenStax 1.2). Phone-call lengths of 2.4, 7.5 and 11.0 minutes are the textbook example. A real-world source of measured data is the CDC’s National Health and Nutrition Examination Survey (NHANES), a national survey that measures the health and nutrition of adults and children in the United States; its mobile exam centers collect dental exams and health and body measurements (CDC NCHS).

Interval vs ratio quantitative data

OpenStax 1.3 describes interval data as having a definite ordering and meaningful differences between values; Celsius and Fahrenheit are its examples. Ratio data are “like interval scale data, but there is a minimum value and ratios can be calculated.” Exam scores of 80, 68, 20 and 92 are its ratio example. Nominal and ordinal data, by contrast, are not quantitative: nominal “cannot be used in calculations”, and ordinal data can be ordered but also allow no calculations. The full four-level framework is in levels of measurement.

Worked example with the arithmetic shown

Illustrative numbers invented for this page, not from a real study.

Mean of counted data

A researcher records the number of phone calls on five days: 0, 3, 2, 4, 2.

Sum = 0 + 3 + 2 + 4 + 2 = 11. Mean = 11 / 5 = 2.2 calls per day.

The data are discrete, but the mean is not: no single day had 2.2 calls. A mean describes the set, so it can fall between countable values.

Mean of measured data

Using OpenStax’s three call lengths: 2.4 + 7.5 + 11.0 = 20.9 minutes. Mean = 20.9 / 3 = 6.9667, reported as about 6.97 minutes.

Why a ratio statement works for exam scores but not for Celsius

For the ratio-scale exam scores 80 and 20: 80 / 20 = 4, so a score of 80 is four times a score of 20, because the scale has a minimum value and ratios can be calculated (OpenStax 1.3).

For Celsius, take 20 degrees C and 10 degrees C. The quotient 20 / 10 = 2 looks like “twice as warm”, but it is an artifact of where the scale puts zero. Converting both to kelvin (0 degrees C = 273.15 K) gives 293.15 K and 283.15 K, and 293.15 / 283.15 = 1.035. The difference of 10 degrees is meaningful on an interval scale; the ratio is not.

Interpretation: what you can do with each type

Scale	Meaningful differences	Meaningful ratios	Source
Interval	Yes	No (no true minimum)	OpenStax 1.3
Ratio	Yes	Yes	OpenStax 1.3

Discrete and continuous describe how the numbers arise, not what you may compute. A mean works for both, as the examples above show.

Common mistakes with quantitative data

• Treating numerals as quantities. OpenStax’s rule is that quantitative data result from counting or measuring an attribute. A code that merely labels a category does not, however numeric it looks. See the “numbers that are still qualitative” discussion in qualitative data and the nominal and ordinal types in categorical variable examples.
• Computing ratios on interval data. “Twice as warm” fails on Celsius, as shown above.
• Rounding discrete means to whole numbers. The 2.2 calls per day above is a valid mean; forcing it to 2 discards information.
• Mixing up the two axes. Discrete vs continuous (counted or measured) and interval vs ratio (scale) are separate questions; a variable has an answer to each.

For quantitative summaries, see descriptive vs inferential statistics; to relate two quantitative variables, see the correlation formula.

Formula for the mean, with every symbol explained

M = Σx / n

• M is the mean.
• Σx (sigma x) is the sum of all the values: for the five daily call counts, 0 + 3 + 2 + 4 + 2 = 11.
• n is the number of values: here 5.

So M = 11 / 5 = 2.2.

How to report it (APA example)

The APA Numbers and Statistics Guide (7th edition) says to use the symbol with a mathematical operator (its example is M = 7.7), to put a space before and after the operator, and to italicize letters used as statistical symbols. It also says not to define standard symbols such as M and n. It asks for means and standard deviations of data on integer scales to be reported to one decimal and other means to two decimals; 2.2 has one decimal.

For the call-count example, a report would read: M = 2.2 calls per day, n = 5.

In running text: “Participants made 2.2 calls per day on average (M = 2.2, n = 5).” The guide also says to use the term rather than the symbol for statistics in running text, for example “the means were”.

Calculate the mean in Excel, R or Python

All three use the five daily call counts from the worked example and return 2.2.

Excel:   =AVERAGE(A1:A5)        (values 0, 3, 2, 4, 2 in A1:A5)
R:       mean(c(0, 3, 2, 4, 2))
Python:  import statistics
         statistics.mean([0, 3, 2, 4, 2])

In Excel, =COUNT(A1:A5) returns 5, the number of numeric entries; text-coded categories are not counted by it.

FAQ

What is quantitative data in simple terms?

Numbers that result from counting or measuring, such as weight, pulse rate or the number of people in a town (OpenStax 1.2).

What is the difference between discrete and continuous quantitative data?

Discrete data are counted (0, 1, 2, 3 phone calls); continuous data are measured and can take fractions or decimals (call lengths of 2.4, 7.5 and 11.0 minutes).

What is the difference between interval and ratio data?

Both allow meaningful differences, but only ratio data have a minimum value and support ratios. Celsius is interval; exam scores are OpenStax’s ratio example.

Is qualitative data ever a number?

Numerals can label categories, and then the data are categorical rather than quantitative. The test is whether the number results from counting or measuring an attribute.

Sources

• OpenStax, Introductory Statistics 2e, section 1.2: Data, Sampling, and Variation in Data and Sampling (checked 2026-10-29).
• OpenStax, Introductory Statistics 2e, section 1.3: Frequency, Frequency Tables, and Levels of Measurement (checked 2026-10-29).
• American Psychological Association, Numbers and Statistics Guide, 7th edition (checked 2026-10-29).
• CDC National Center for Health Statistics, About NHANES (checked 2026-10-29).