Quantitative Data

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

In statistics, quantitative data is numerical and acquired through counting or measuring and contrasted with qualitative data sets, which describe attributes of objects but do not contain numbers. 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.

Additionally, quantitative data can further be broken down and analyzed according to the level of measurement involved including nominal, ordinal, interval, and ratio levels of measurement or whether or not the data sets are continuous or discrete.

Levels of Measurement

In statistics, there's a variety of ways in which quantities or attributes of objects can be measured and calculated, all of which involve numbers in quantitative data sets. These data sets do not always involve numbers that can be calculated, which is determined by each data sets' 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.

Determining which of these levels of measurement a data set falls under will help statisticians determine whether or not the data is useful in making calculations or observing a set of data as it stands.

Discrete and Continuous

Another way that quantitative data can be classified is whether the data sets are discrete or continuous—each of these terms has 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 objects that are only useful while whole like chairs or books.

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.