Patterns in the structure of data
There are many different contexts in which data are recorded and we have stressed the importance of context to a statistician. However the statistical methods that can be used on the data depend less on the context than on the internal structure of the data.
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All three data sets above have the same basic structure — there are 12 numerical measurements that have been made from 12 different 'individuals' (people, districts or days) and these individuals have been classified into one of two groups. The same statistical methods can be applied to all three data sets.
Variables and 'individuals'
Although data can have a very rich structure, most data structures are fairly simple.
Most commonly, one or more measurements is recorded from each of a collection of 'individuals' (also called 'cases' or 'units'). These 'individuals' may be people, but could equally be companies, houses, containers of milk, computers, days or any other units from which measurements can be made. The data can therefore be presented in a rectangular array called a data matrix.
The different measurements are called variables. The variables may describe closely related characteristics of the individuals (e.g. student marks in the three assignments in a statistics course) but the measurements can be more distinct and may even have different units (e.g. age in years, annual salary in dollars and number of days taken off work through illness in the last year, each recorded from all employees in a company).
Salaries for Managers
When considering which career to pursue, one important factor is the likely salary. The table below shows average salaries for five different types of manager in 2012, as published by the US Department of Labor.
Type of Manager | Mean salary in 2012 |
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Marketing Manager | $129,870 |
Sales Manager | $119,980 |
Financial Manager | $123,260 |
Human Resources Manager | $109,590 |
Industrial Production Manager | $97,490 |
There is however considerable variation in salaries within the USA. The diagram below shows the mean salaries within each of the 48 states in continental USA, plus Washington DC.
Each state is an 'individual' and the five mean salaries in the states are variables. Click on states in the map to observe how each state corresponds to a row in the data array.
Click on the icons representing the five types of salary at the top right of the diagram, and observe how each type of measurement corresponds to a column in the data array.