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Data (Mathematics Glossary)

What Is Data?

Data is a set of facts (such as numbers, measurements or words) that have been collected or measured. Data can be reported, visualized and analyzed to help us learn and make decisions.

Dictionary Definition

The Merriam-Webster dictionary defines data as "factual information (such as measurements or statistics) used as a basis for reasoning, discussion, or calculation."

Real Examples of Data

When we want to understand something about the world, we collect data about it.
  • Imagine a teacher wanted to find out about how well a mathematics class is doing. The teacher would collect the classes' test scores:



    The test scores are data.

  • Imagine you wanted to know the typical heights of people. You could measure the heights of people.



    The heights are data.

  • Imagine you wanted to know how many of each shape you had. You could observe which shapes you have.



    The shapes are data.

Types of Data

There are different types of data.
  • The main distinction is between qualitative (words) and quantitative (numbers) data.



    • Test scores and the heights are both quantitative data (because we use numbers to describe them).

    • Shapes are qualitative data (because we use words to describe them).

  • There are also two types of quantitative data: discrete and continuous data.

    • Discrete data can only take certain values, like whole numbers (1, 2, 3...). Discrete data can (often) be counted.

      Test scores are discrete data. Test scores can only take whole numbers.

    • Continuous data can take any value (within a range). Continuous data can (often) be measured.

      Heights are continous data. A person could be 5 feet and 9½ inches. They don't have to be a whole number of feet or inches.
Read more about types of data
Read more about qualitative data
Read more about quantitative data
Read more about discrete data
Read more about continuous data

Using Data

Data can be summarized using averages:



Data can also be presented in tables and graphs:



Interactive Test
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Here's a second test on data.
Here's a third test on data.
Note

Datum and Data

A single value is called a datum. For instance, a single test score would be a datum.

When there are more than one value, it is data. Data is plural. The test scores of a class are data.

Data also means the entire set of values, so it is still correct to say "the data is".

What's in a Name?

Data comes from the Latin word 'datum', meaning a 'thing that is given'. It is the past form of 'dare', which means 'to give'.

This is because when we collect facts, they are already given to us. A student's test score or a person's height are not something we create, they are already there. They can be counted or measured to be used as data.

Top Tip

Quantitative = Quantity

Quantitative data deals with quantities (numbers).