# Australian Bureau of Statistics

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 Education Services

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 Concepts and definitions

Click on the triangles to open a section. The table below is a list of the concepts covered in each section.

Statistics

Statistics are numerical data that have been organised to serve a useful purpose. A major role of the ABS is to provide the Australian community with statistics that will help them make informed decisions. Statistical information provided by the ABS is used widely in Australia by governments, business people, researchers, members of the public, teachers and students.

Data
Data are observations or facts which, when collected, organised and evaluated, become information or knowledge.

Data item
A data item is the smallest piece of information that can be obtained from a survey or census.

Dataset
A dataset is data collected for a particular study. A dataset represents a collection of elements; and for each element, information on one or more characteristics is included.

Outliers
An outlier is an extreme value of the data. It is an observation value that is significantly different from the rest of the data. There may be more than one outlier in a set of data.
Sometimes, outliers are significant pieces of data and should not be ignored. In other instances, they occur as a result of an error or misinformation and should be ignored. The decision to include or exclude an outlier needs to be clearly justified when discussing results.

Example:
The weights (in kilograms) of 30 students were measured and recorded in the stem and leaf plot shown in Figure 1. In this case, the stem is the whole number values and the leaves are the decimal values. The outliers are 56.3 and 67.7.

 Stem Leaf 56 3 57 58 4 4 9 59 0 0 2 3 8 60 0 2 4 5 7 8 9 61 1 2 4 4 5 6 7 9 9 62 1 2 3 7 63 64 65 7
Fig 1 Stem and leaf plot

Variables

 A variable is any measurable characteristic or attribute that can have different values for different subjects. Height, age, amount of income, country of birth, grades obtained at school and type of housing are examples of variables. Observation An observation is a single piece of data about a variable Independent variable An independent variable is the variable whose values are independent of changes in the values of other variables. It its the variable deliberately controlled or changed to assess changes in the dependent variable. Dependent variable A dependent variable depends on the independent variable. Categorical variables Nominal variable A nominal variable describes a name or category. For example, for the variable 'method of travel to school' all its values are words such as bus, walk, car and tram. Nominal variables are often referred to as categorical variables. Ordinal variable An ordinal variable is a number that represents a category. For example, postcodes and school year levels. Numerical variables A numerical variable is one that describes a numerically measured value. Numerical variables can be either discrete or continuous. Continuous variable A continuous variable is a numeric variable that can take any value within a certain range. For example, distance, age and temperature are continuous variables. Discrete variable A discrete variable can only take a finite number of values within a certain range. An example of a discrete variable is the number of children in a family – a family can have 0,1,2 or 3 children but not 2.5. Class interval A class interval is a group of data values for a variable. The intervals are generally the same size – for example, 4-6, 7-9 and 10-12. However, the intervals may have different sizes such as 4-6, 7-9 and 10-14. The boundaries of class intervals must not overlap so that each observation can be allocated to only one interval.

Sampling
Frequency and distribution

 The frequency (f) of a particular observation is the number of times the observation occurs in that data. Cumulative frequency Cumulative frequency is the total of a frequency and all frequencies below it in a frequency distribution. It is the running total of frequencies. Relative frequency Relative frequency is another term for proportion. It is the number of times a particular observations occurs divided by the total number of observations. Distribution The distribution of a variable is the pattern of values of the observations.

Graphs and displays

Graph
A graph is a diagram representing a system of connections or interrelations among two or more variables by a number of distinctive dots, lines, bars, etc.

Chart
A chart is a visual representation of data. Bar, line, pie and other types of charts are examples of charts.

Box and whisker plots (often called ‘box plots’) can be used to show the interquartile range. Figure 1 shows a box and whisker plot of student ages.
Notice that a scale is drawn underneath. Box plots can be drawn horizontally or vertically.

Frequency distribution tables can be used for nominal and numeric variables.

Example:
Twenty people were asked how many cars were registered to their households. The results were recorded as follows: 1, 2, 1, 0, 3, 4, 0, 1, 1, 1, 2, 2, 3, 2, 3, 2, 1, 4, 0, 0. This data can be presented in a frequency distribution table – see Figure 2.

Stem and leaf plots are a convenient way to organise data. Each observation value is considered to consist of two parts - a stem and a leaf.

• the stem is the first digit or digits
• the leaf is the final digit

Example:
The number of books ten students read in one year were as follows: 12, 23, 19, 6, 10, 7, 15, 25, 21, 12.
In ascending order, these are: 6, 7, 10, 12, 12, 15, 19, 21, 23, 25. Figure 3 is a stem and leaf plot of this data.

In the stem and leaf plot (fig 3):

• the stem '0' represents the class interval 0-9
• the stem '1' represents the class interval 10-19
• the stem '2' represents the class interval 20-29.

If there are a large number of observations for each stem, the stem can be split in two. For example the interval 0-9 could be split into intervals 0-4 and 5-9. The stem would then be written as 0(0) and 0(5).

Time series
A time series is a collection of observations of well-defined data items obtained through repeated measurements over time. For example, measuring the value of retail sales each month of the year would comprise a time series.

Trend
The ABS defines a trend as the long term movement in a time series without calendar related and irregular effects, and is a reflection of the underlying change in that measure. It is the result of influences such as population growth, price inflation and general economic changes.

Fig 1 Box and whisker plot

 Number of cars (x) Tally Frequency (f) 0 l l l l 4 1 l l l l l 6 2 l l l l 5 3 l l l 3 4 l l 2
Fig 2 Frequency distribution table

 Stem Leaf 0 1 2 6 7 0 2 2 5 9 1 3 5
Fig 3 Stem and leaf plot

Summary statistics