Analysing the data

Data management tasks
Using computer software
Where computers are not available

Data management tasks

Once a set of data has been obtained, it is time to begin analysing it. This means engaging in some or all of the following activities:

• organizing the data into tables
• calculating percentages
• calculating measures of central tendency
• constructing graphs

In addition to performing these mechanical tasks, students are required to think about the meaning of the data.

For example, they can explore the relationship between two variables or observe the effect that removing extreme values has upon the mean or the median. Most provincial curricula for Grades 7 and 8 specify that students will engage in a set of skills in the data management strand which include

• collecting and organizing categorical, discrete and continuous data
• displaying data in relative frequency tables, bar graphs, circle graphs, histograms, etc.
• identifying bias in data
• relating changes in data to changes in central tendency
• making inferences based on data

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Using computer software

Many software programs will do most of the mechanical work of creating tables, performing calculations and constructing graphs with just a few clicks of the mouse. By eliminating the slow and often tedious work that can act as a barrier, these programs allow students to quickly progress to deriving meaning from the data.

Students can use computer software to question the data and experiment with different types of graphs that represent them or to examine the relationships between variables. This means that within a single class period, students as young as Grade 4 can find meaning in the data without having to spend the entire time working on a single graph. Additionally, since most students enjoy using technology, they are having fun while they are working.

If you have limited access to technology, some of the best exploration of data comes in small group settings where students can ask each other their 'I wonder if …' questions and work through them as a community of learners. For this reason, you don't need to have one computer per student. Many data management activities lend themselves to learning in pairs or groups of four. This means that four to six computers can be enough for a lesson.

Many software programs are used by the various school boards across Canada. The list below provides an overview of the most commonly used programs, but is by no means complete. Please note that Statistics Canada does not endorse the use of any particular program.

Software for data management can be categorized into these subgroups:

• spreadsheet programs
• dynamic statistical software
• dynamic graphing software
• graphing calculator software

Spreadsheet programs

Examples:

Excel (Grades 4 to 12)

QuattroPro (Grades 4 to 12)

AppleWorks (Grades 4 to 12)

Calc in Open Office (Grades 4 to 12)

Data imported into a spreadsheet program are displayed in a table consisting of rows and columns. Quick calculations of data ranges, column totals, means and percentages can be obtained by entering formulae into the appropriate cells. Some programs allow one-click options for certain calculations.

To graph the data, use the graphing tool provided in your spreadsheet program. For categorical data, you must first make a frequency table before creating the graph. In addition, Excel also offers a pivot chart option.  

The graphing tool lets students select a type of graph and personalize it with their choice of colour, font, type size, etc. See Types of Data to find appropriate types of graphs for different types of data.

Dynamic statistical software

Examples:

TinkerPlots (Grades 4 to 8)

Fathom (Grades 8 to 12)

Data are imported into these programs by cutting and pasting a URL address or by importing a spreadsheet file in comma separated values (.csv) or plain text (.txt) formats. The data appear as a list of attributes in a data card, which you can transfer into a graph by the drag-and-drop method. Each point on the graph represents the response of one individual in the sample. That individual's entire set of attributes can be brought up by clicking on the data point.

Students may pose a question and then create one or two different graphs simply by dragging columns of data onto the axes. They can pose a different question, then drag in a different column and see the changes immediately.

These are some of the graph types available in these programs:

• Dot plot (stacked or unstacked)
• Line plot
• Histogram
• Box plot
• Bar chart
• Scatter plot

Dynamic graphing software

Example:

EasyGraph (Grades 8 to 12)

Graphing software is useful for exploring relationships between two variables. Data are entered point by point on a Cartesian grid (x- and y-axes), creating a scatter plot diagram. Program features include finding the line of best fit through the points and obtaining an instant summary of statistical measures (mean, variance and standard deviation). Students can investigate the effect that eliminating outliers may have on the shape of the graph or the mean.

Graphing calculator software

Example:

TI-Interactive or TI-Connect for use with TI graphing calculator (Grades 7 to 12)

Graphing calculators allow students to explore the relationship between two variables. Students can either manually enter the data for each variable into a table of values or import them using a link cable.

The graphing calculator can graph data as a scatter plot and will provide lines of best fit and statistical measures (mean, variance and standard deviation). Most provincial curricula require the use of graphing calculators for certain math courses from Grades 8 to 11.

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Where computers are not available

In many schools, computers and software programs are not always available, so it is necessary to do much of the work by hand. Even when computers are readily available, it may be preferable for students to do the work by hand for certain parts of the curriculum. By going through the manual steps themselves, students can understand the concepts involved in creating tables and graphs and calculating statistical measures.

Many valuable activities are available for working with data by hand. The list below offers a selection of them that you can print or download from the Internet. Note that in some cases, you will also need to print selected data from a spreadsheet before beginning the activity so that the students can have a hard copy to work with.

Activities that don't require computers

You are the researcher! (Grades 4 to 8)
This mini-project asks students to decide on an interesting question to research using their Census at School class results. They then display the results using different types of graphs.

Worksheets for analysing class data (Grades 9 to 12)
These activities use Censusat School class data to cover frequency tables, measures of central tendency, circle graphs, histograms, lines of best fit, etc. A marking rubric is included. 

Note: In the last activity, students are asked to compare their handmade line of best fit with one created on a graphing calculator. You can easily omit this section if graphing calculators are not available.

Other Census at School learning activities (Grades 4 to 12)
These activities make use of Census at School class results in the math, social science and health curricula. While some lessons ask students to retrieve Canadian or international data from the website using computers, most only require that the teacher print selected columns from the class data prior to the activity.

Examples of lesson titles:

Travel to school (Grades 4 to 8): Analyse the data using stem and leaf plots and pie charts.

What a zoo! (Grades 4 to 8): Examine bar graphs that represent the same data but use different scales.

The Vitruvian theory—does it apply to you? (Grades 4 to 8 and Grades 9 to 12): Verify the theory described by Leonardo Da Vinci that arm span is equal to height.

E−STAT lesson plans (Grades 7 to 12)

These activities make use of E−STAT data in the math, social science and health curricula. Complete student instructions and worksheets are included. While most lessons in this section ask students to use computers to retrieve data tables from E−STAT, the teacher can easily print the tables and distribute them to students before the activity.

Examples of lesson titles:

Comparing the food choices and body image of 15-year-olds around the world (Grades 7 to 12): Examine and compare data from various countries .

Role playing Jean Talon (Grades 7 to 9): Taking the role of Jean Talon, use 1665 census data to convince the King of France to increase investments in New France.

Smoking today = smoking tomorrow (Grades 7 to 9): Research trends by examining smoking data by age and gender.