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It is assumed that students are now familiar with categorical, count and measurement data, have had learning experiences in recording, classifying and exploring individual datasets of each type, and have seen and used tables, picture graphs and column graphs for categorical data and count data with a small number of different counts treated as categories, and dotplots of measurement and count data.
It is assumed that focus in exploration and comment on measurement and count data has been on each set of data by itself, but that in Year 6, students have become familiar with considering more than one set of categorical data on the same subjects. In doing so, they met the concept of statistical variables and understood that they were investigating data on pairs of categorical variables.
Hence the need to develop statistical skills and thinking across all levels of education has grown and is of core importance in a century which will place even greater demands on society for statistical capabilities throughout industry, government and education.
A natural environment for learning statistical thinking is through experiencing the process of carrying out real statistical data investigations from first thoughts, through planning, collecting and exploring data, to reporting on its features.
Statistical data investigations also provide ideal conditions for active learning, hands-on experience and problem-solving. No matter how it is described, the elements of the statistical data investigation process are accessible across all educational levels.
Real statistical data investigations involve a number of components: No matter how the statistical data investigative process is described, its elements provide a practical framework for demonstrating and learning statistical thinking, as well as experiential learning in which statistical concepts, techniques and tools can be gradually introduced, developed, applied and extended as students move through schooling.
Because these data types are quantitative, investigation and interpretation include considerations of representations and summaries of size and variation in size of observations.
In previous years, we have considered different types of data. You can think of a statistical variable as a description of an entity that is being observed or is going to be observed. Hence when we consider types of data, we are also considering types of variables.
Some examples of measurement data are: Measurement data have units of measurement and are recorded with a certain precision that depends on the measuring instrument, the choice of the investigator and practical restrictions.
Measurement variables are examples of continuous variables; continuous variables can take any values in intervals. For example, if someone says their height is cm, they mean their height lies between If they say their height is If someone reports their age as 12 years, they usually mean their age is in between 12 and 13 years.
Note the convention with age is that the interval is from our age in whole number of years up to the next whole number of years.
If someone says their age is 12 and a half, is there a standard way of interpreting the interval they are referring to? Do they mean A count variable counts the number of items or people in a specified time or place or occasion or group. Each observation in a set of count data is a count value.
Count data occur in considering situations such as: Also, the sizes of the observations will tend to be large, sometimes very large. For these types of count variables, the types of graphs and summaries used for continuous variables are often appropriate.
This module uses a number of examples of continuous data or count data with many values to introduce one of the graphs that group values into intervals the stem and leaf plot and some quantities that are calculated from data and that represent certain features of data.
Such quantities are called summary statistics. The examples and new content are developed within the statistical data investigation process through the following: Such phases lend themselves to representation on a diagram, as follows.
The examples consider simple situations familiar and accessible to Year 7 students and in reports in digital media and elsewhere, and build on the situations considered in F- 5. The module also includes tips on possibly misleading aspects of summaries of continuous data.
Initial questions that can motivate an investigation The following are some examples that involve collecting, or accessing, or finding, and investigating data for at least one continuous or large count variable.
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