Learning aims:

Processing and representing data, using ICT as appropriate
Use ICT to generate pie charts
Interpreting and discussing results
Interpret diagrams and graphs including pie charts, and draw simple conclusions based on the shape of graphs and simple statistics for a single distribution.

Preparation:

Display the Charting software using a data projector (and interactive whiteboard if available).
If laptops are available, students could use the software to explore pie charts for themselves.

Charting setup: Input the following set of numbers into List 1 to represent the total numbers of students travelling to school by different types of transport. Ideally, carry out a quick classroom survey at the end of the previous lesson to collect this data from the class. However, choose the total number of students in the survey to be a factor of 360˚ when introducing pie charts to support students to see the connections between the angle at the centre for each sector and the number of students the sector represents.
Display the Pie chart for List 1.

Additional resources:
Some printed copies of the pie chart for students to work with.

Activity

Questions to ask students

Display the pie chart on the board, and give the students a paper copy.

Ask students to link the data in the table with the sections of the pie chart and annotate their paper copies.

Discuss the various strategies that they used which may include using the colour coding, observing the largest and smallest sections, working out that the data is presented clockwise etc.

Which section of the pie chart links with which data from the table?

How did you know which section was which?

Begin by discussing the students’ estimates of the angles at the centre for each sector of the pie chart.

Encourage students to annotate their paper copies and provide protractors if asked for!

Discuss the students’ suggestions as to how the computer has worked out the exact values.

Using what you know about angles, can you discuss with your partner an estimate of the size of the angles at the centre for each sector in the pie chart?

How do you think the computer software has calculated these?

Roll the cursor over the pie chart to reveal the calculated angles and put these numbers in List 2 of the table alongside the corresponding numbers in List 1.

Discuss with students the sum of the angles equalling 360˚, and the fact that they are in proportion with the frequencies in List 1.

What do you notice about the numbers in List 2?

It is helpful to have a large paper copy of a circle divided into 30 (in this case) equal sectors.

For less able groups, pass the paper around the group and ask each student to shade their means of transport to school using the same colour code as the software. Discuss how the software automatically puts the same colours together to build up the large sections of colour.

If there are 30 students in the survey, and each of them gets an equal share of the pie chart, how can we calculate what share of the pie chart each student represents?

Provide students with several small data sets to use the software to create pie charts using the software and answer questions that require them to interpret the data in the tables.

Learning aims:

Interpreting and discussing results
Compare two or more distributions and make inferences, using the shape of the distributions, the range of data and appropriate statistics.

Preparation:

Display the Charting software using a data projector (and interactive whiteboard if available).
In this activity, students should use the software to explore box and whisker plots for themselves.

Charting setup: Open a blank Charting page and select the “Raw” data option.

Additional resources: Paper copies of the Box and whisker plots student task sheet.

Activity

Questions to ask students

Enter the following list of eight numbers into List 1.

1 1 2 3 5 8 8 10

Display the Box and whisker plot for List 1.

Give students plenty of opportunity to discuss the Box and whisker plot, what the marks represent.

Reveal the data values for the minimum, lower quartile, median, upper quartile and maximum.

Students are likely to be most familiar with the minimum, median and maximum, so discuss these first and explain how the lower and upper quartiles have been calculated.

What do you think this graph is showing?

Give students a copy of the task sheet.

They will need to use the software to conjecture (predict) which numbers produced each of the Box and whisker plots and text their conjectures using the software.

Hold a plenary session during which you encourage students to share the strategies that they used to attempt to solve the third problem.

What other information would they need to confirm their decisions?

Problem 1:

Eight numbers produce the following Box and whisker plot.
The mean average of the eight numbers is 6.75

What could the eight numbers be?
Is it possible to find another solution? Justify your decision!

Problem 2:

A different set of eight numbers produce the following Box and whisker plot.

What could the eight numbers be?
Can you find another solution?

Problem 3:

Seven numbers have the following statistical information.
Minimum = 2
Maximum = 12
Mean average = 7

Draw the Box and whisker plot for this set of numbers?
Could there be more than one solution?