Statistics data cards are a physical resource used by students to learn about statistics and statistical investigations. Data cards are used to teach statistical analysis, how to create graphs and tables, and sampling. They are used for a wide range of ages and develop understanding of subtle and difficult concepts.
A data card
Each data card corresponds to an object which could also be stored as one row or entry in a database. That is, each card contains multivariate information for a different observation, individual or sampling unit about the same attributes or measurements.
The layout of the cards needs to be consistent. The information about the same attribute or measurement needs to be in the same place on each card. Colours and other visual effects are often used to highlight different data values. Sometimes some of the data can be shown in a visual way, requiring the student to count, measure or otherwise extract the data from an image.
The data cards can be made from paper or card and are sometimes laminated. Data cards can be made by the students themselves, by the teacher or purchased as a teaching resource.
The figure below shows three examples of data cards.
Dragonistics Dragon data cards
Four-element data cards
List-based data cards
The data represented
The data represented by the data cards might be from a sample or population. This depends on the purpose of the lesson, where the data is from and what it represents. The same data cards might be treated as a sample in one instance and as a population in another.
At the earliest levels students learn about data and ways it can be manipulated to gain information from the data. Data cards hold multivariate data about individuals. A set of cards, together, holds information about a group. Sorting and organising a set of cards helps students learn the concepts of multivariate data and variability within data.
The data cards can be used to form physical tables and graphs. This physical activity helps students understand the relationship between individual data points and the data displays. This enables understanding of what the data displays represent. For example, each data card in a physical bar chart adds a fixed amount to the height of a bar.
When different groups of students are given different sets of data cards to analyse in the classroom, each group will find slightly different results, based on their own set of cards. Students understand this intuitively, and it helps to develop the very important concept of variability between samples. The similarities between the results can help students see that samples can be used to infer properties of the population.
With enough data cards, maybe 200 or 500 or more, it is not practical to analyse all of the cards. Treating all of the cards as a population and analysing only a sample of the cards teaches concepts of sampling and inference. With such a 'large' population the need for sampling becomes obvious.
Data cards can also be used to teach bootstrapping concepts.
Dragonistics data cards are available from the Statistics Learning Centre online shop.