Lesson

In Unit 2 we studied statistics with univariate data. 'Uni' means one (think unicycle) so if we want to observe and analyse changes in a single variable then this is univariate statistics. For example, comparing two student's test results by comparing the mean and standard deviation of each set is working with a single variable (test results) so it is univariate.

In Unit 3 our focus will be statistics with bivariate data. 'Bi' means two (think bicycle) so if we are interested in comparing or finding an association between two sets of different variables then this is bivariate statistics. For example, looking at the association between litres of soft drink consumed per week and BMI for a set of people is working with bivariate data as there are two variables (litres and BMI).

In statistics, a 'variable' refers to a characteristic of data that is measurable or observable. A variable could be something like temperature, mass, height, make of car, type of animal or goals scored.

Data variables can be defined as either **numerical** or **categorical**.

- Numerical data is where each data point is represented by a
**number**. Examples include: number of items sold each month, daily temperatures, heights of people, and ages of a population. The data can be further defined as either discrete (associated with counting) or continuous (associated with measuring). Numerical data is also known as**quantitative**data.

- Categorical data is where each data point is represented by a
**word**or label. Examples include: brand names, types of animals, favourite colours, and names of countries. The data can be further defined as either ordinal (it can be ordered) or nominal (un-ordered). Categorical data is also known as**qualitative**data.

**Discrete numerical data**

Discrete numerical data involve data points that are distinct and separate from each other. There is a definite 'gap' separating one data point from the next. Discrete data usually, but not always, consists of whole numbers, and is often collected by some form of **counting**.

Examples of discrete data: number of goals scored per match ($1$1, $3$3, $0$0, $5$5, etc) , number of children per family ($0$0, $1$1, $2$2, $3$3, etc), shoe size ($6$6, $6\frac{1}{2}$612, $7$7, $7\frac{1}{2}$712, etc)

**Continuous numerical data**

Continuous numerical data involves data points that can occur anywhere along a continuum. Any value is possible within a range of values. Continuous data often involves the use of decimal numbers, and is often collected using some form of **measurement**.

Examples of continuous data: height of trees in metres ($12.357$12.357, $14.022$14.022, $13.454$13.454, etc), times taken to run ten km in minutes ($55.34$55.34, $58.45$58.45, $61.29$61.29, etc), daily temperature in degrees C ($31.2$31.2, $29.4$29.4, $30.4$30.4, etc)

**Ordinal categorical data**

The word 'ordinal' means 'ordered'. Ordinal categorical data involves data points, consisting of words or labels, that can be **ordered** or ranked in some way.

Examples of ordinal data: product rating on a survey (good, satisfactory, excellent), Level of achievement (high distinction, distinction, credit, pass, fail)

**Nominal categorical data**

The word 'nominal' means 'name'. Nominal categorical data consists of words or labels, that **name** individual data points that have no clear rank order.

Example of nominal data: Nationalities in a team (German, Austrian, Italian, Spanish, etc), eye colour (grey, blue, brown, green, etc)

A scientist collects data on iron levels in soil and growth of a type of weed in order to investigate the relationship between them.

Is this an example of univariate data or bivariate data?

Univariate data

ABivariate data

BUnivariate data

ABivariate data

B

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

Which of the following variables can be classified as ordinal categorical?

Length of a pencil in mm

ATime taken to get to school in minutes

BWeight of dogs in kg

CDriving license status (learner, red P, etc)

DHair colour (black, red, blonde, etc)

EHourly rate of pay

FLength of a pencil in mm

ATime taken to get to school in minutes

BWeight of dogs in kg

CDriving license status (learner, red P, etc)

DHair colour (black, red, blonde, etc)

EHourly rate of pay

F

review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results