New Zealand
Level 6 - NCEA Level 1

# Types of Data

Lesson

## Numerical data

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

Numerical data can be either continuous or discrete.

### Continuous Data

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.

### Discrete Data

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

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.

### Ordinal data

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 data

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.

#### Worked Examples

##### QUESTION 1

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

1. favourite flavours

A

maximum temperature

B

daily temperature

C

types of horses

D

favourite flavours

A

maximum temperature

B

daily temperature

C

types of horses

D

##### QUESTION 2

Which one of the following data types is discrete?

1. The number of classrooms in your school

A

Daily humidity

B

The ages of a group of people

C

The time taken to run $200$200 metres

D

The number of classrooms in your school

A

Daily humidity

B

The ages of a group of people

C

The time taken to run $200$200 metres

D

##### Question 3

Classify this data into its correct category:

Weights of dogs

1. Categorical Nominal

A

Categorical Ordinal

B

Numerical Discrete

C

Numerical Continuous

D

Categorical Nominal

A

Categorical Ordinal

B

Numerical Discrete

C

Numerical Continuous

D

### Outcomes

#### S6-1

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.

#### 91035

Investigate a given multivariate data set using the statistical enquiry cycle