Language and Use of Statistics

NZ Level 6 (NZC) Level 1 (NCEA)

Types of Data

Lesson

Numerical data can be counted, ordered and measured. It is also called quantitative data.

Numerical data can be either continuous or discrete.

A data set is continuous if the values can take on any value within a finite or infinite interval.

Examples of continuous data are height, weight, temperature or the time taken to run $100$100 metres.

Do you notice how all these examples could be anywhere on a scale interval and could even be fractions? For example, it might be $25.3$25.3 degrees or a man might be $182.13$182.13cm tall.

A data set is discrete if the numerical values can be counted but are distinct and separate from each other. They are often (but not always) whole number values.

Example of discrete data: the number of goals scored in a game, the number of people in a class, the number of pets people have.

Do you notice how all these examples have distinct values? For example, you couldn't score $2.5$2.5 goals in a game of soccer or own $\frac{1}{4}$14 of a dog so there is no continuity between the scores.

However, in some tournaments, half a point is awarded for a draw. In this case, there could be a score of $2.5$2.5, but there still could not be a score of $2.25$2.25 or $2.75$2.75 so the data is still discrete.

Categorical data is non-numerical. In other words, it describes the qualities or characteristics of a data set. It is also called categorical data. Categorical data is also known as qualitative data.

There are two types of categorical data: ordinal and nominal.

A set of data is ordinal if the values can be counted and ordered but **not **measured.

Rating scales are examples of ordinal data. The finishing places in a race are another example of ordinal data. Think about it- the positions in a race can be ordered or ranked. Finishing first means you were faster than the person who came second and the person who finished eighth was slower than the person who finished sixth. However, the differences between the finishing times may not be the same between all competitors. Check out the picture below. The times between first and second will be really close- maybe less than half a second. However, the time between second and third may be more than a second. There is not a fixed interval.

*Nominal* basically means *name*. In other words, data is split up based on different names or characteristics. Nominal data may be the names of countries you have visited or your favourite colours. We could assign these different characteristics a number where the numbers are labels. In other words, you are giving categorical data numerical labels. You can count but **not **order or measure nominal data.

Which of the following are examples of numerical data? (Select all that apply)

favourite flavours

Amaximum temperature

Bdaily temperature

Ctypes of horses

Dfavourite flavours

Amaximum temperature

Bdaily temperature

Ctypes of horses

D

Which one of the following data types is discrete?

The number of classrooms in your school

ADaily humidity

BThe ages of a group of people

CThe time taken to run $200$200 metres

DThe number of classrooms in your school

ADaily humidity

BThe ages of a group of people

CThe time taken to run $200$200 metres

D

Classify this data into its correct category:

Weights of dogs

Categorical Nominal

ACategorical Ordinal

BNumerical Discrete

CNumerical Continuous

DCategorical Nominal

ACategorical Ordinal

BNumerical Discrete

CNumerical Continuous

D

Plan and conduct investigations using the statistical enquiry cycle: A justifying the variables and measures used B managing sources of variation, including through the use of random sampling C identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays D making informal inferences about populations from sample data E justifying findings, using displays and measures.

Investigate a given multivariate data set using the statistical enquiry cycle