Quantitative Data

Different numbers representing quantitative data.
Quantitative Data arise in many ways.

Definition:  Quantitative data is numerical and acquired through counting or measuring.

Quantitative data is contrasted with qualitative data. Qualitative data sets do not contain numbers that we can perform mathematics upon.  Qualitative data, also known as categorical data, and are separated by traits or attributes.

Examples of Quantitative Data

There are a variety of ways that quantitative data arises in statistics.

  Each of the following is an example of quantitative data:

  • The heights of players on a football team
  • The number of cars in each row of a parking lot
  • The percent grade of students in a classroom
  • The values of homes in a neighborhood
  • The lifetime of a batch of a certain electronic component.
  • The time spent waiting in line for shoppers at a supermarket.
  • The number of years in school for individuals at a particular location.
  • The weight of eggs taken from a chicken coop on a certain day of the week.

Levels of Measurement

Quantitative data can be analyzed by determining its level of measurement:

  • Nominal - Any numerical values at the nominal level of measurement should not be treated as a quantitative variable.  An example of this would be a jersey number or student ID number.  It makes no sense to do any calculation upon these types of numbers.
  • Ordinal - Quantitative data at the ordinal level of measurement can be ordered, however differences between values are meaningless.  An example of data at this level of measurement is any form of ranking.
  • Interval - Data at the interval level can be ordered and differences can be meaningfully calculated.  However data at this level typically lacks a starting point.  Moreover, ratios between data values are meaningless.  For example, 90 degrees Fahrenheit is not three times as hot as when it is 30 degrees.
  • Ratio - Data at the ratio level of measurement can not only be ordered and subtracted, but it may also be divided.  The reason for this is that this data does have a zero value or starting point.  For example, the Kelvin temperature scale does have an absolute zero.

Discrete and Continuous

Another way that quantitative data can be classified is whether the data are discrete or continuous.  Each of these terms have entire subfields of mathematics dedicated to studying them.  It is important to distinguish between discrete and continuous data because different techniques are used.

A data set is discrete if the values can be separated from each other.  The main example of this is the set of natural numbers.  There is no way that a value can be a fraction or between any of the whole numbers.  This set very naturally arises when we are counting.

Continuous data arises when individuals represented in the data set can take on any real number in a  range of values.  For example, weights may be reported not just in kilograms, but also grams, and milligrams, micrograms and so on.  Our data is limited only by the precision of our measuring devices.