In this unit students will identify how to plan and carry out a statistical investigation, looking at facts about their class as a context.
- Write questions for statistical investigations and design a method of collection of data.
- Display collected data in an appropriate format.
- Make statements about implications or possible actions based on the results of an investigation.
- Make conclusions on the basis of statistical investigations.
It is vital when planning statistical investigations that the students understand the importance of the way that they plan, collect, record and present their information. If they are not consistent in the way they carry out any of these steps, they could alter their findings, therefore making their investigation invalid.
In this unit the students will first look at choosing questions to investigate, making sure that the topic lends itself to being investigated statistically. They will then collect their data using tally charts. Once they have collected and recorded their data they will present their findings as bar graphs.
- Paper and pencils
- Presentation materials
Although this unit is set out as five sessions, to cover the topic of statistical investigations in depth will likely take longer. Some of the sessions, especially sessions 4 and 5 dealing with data presentation, could easily be extended as a unit in themselves. Alternatively, this unit could follow on from a unit on data presentation to give students an appreciation of practical applications of data display.
Session 1 provides an introduction to statistical investigations. The class will work together to create a bar chart of numbers of siblings for the class.
Explain to the class that their job for maths this week will be to gather statistics on the class to be presented as a report which will be sent home for parents.
Ask students whether they can explain what the word statistics means.
Explain that statistics are information collected and presented in a way that other people can understand what it shows.
Explain that the class will work in small groups, each of them with the job of finding information about a particular question.
First we will work as a whole class to answer the question:
How many brothers and sisters do people in our class have?
Ask each student how many brothers and sisters they have and to record their answer on a piece of paper (without suggesting any organising structure).
Would the piece of paper would be a good way to show someone else how many brothers and sisters people in the class have?
What would be a better way?
How can we show the information so that people can easily understand what it is showing?
Hopefully someone will suggest a more organised list, or counting the number of 0s, the number of 1s etc and writing sentences to explain how many there are of each.
Carry out these suggestions to show how much clearer they make the information.
Ask for suggestions for other ways to show the information.
If nobody suggests it introduce the idea of bar graphs.
Demonstrate how to draw a bar graph of the information, ensuring that you highlight important features of bar graphs; axes, scale and labels on the axes, title, and accurately plotted bars. Students could draw their own versions as a practice exercise.
Explain that over the next few days students will be investigating some other ideas about the class and making their own graphs to show the information.
This session is ultimately about choosing an appropriate topic to investigate. There will be a real need for discussion about measurable data and realistic topics that can be investigated in the given time frame. It would be a good idea to provide the students with a list of topics, but they should be encouraged to try and come up with something original where possible.
Recap the previous session’s work, discussing how the information was collected and how it was presented.
Explain that in this session students will work in small groups to come up with three questions that they will collect information from the class about so that they can make graphs of it.
Write up a list of criteria that the questions must meet.
- They must be appropriate to ask everyone.
- They must be easy to answer.
- There must be no more than 5 answers that people can give. (Any more would be too messy to graph).
Put students in to small groups and give them a few minutes to come up with some ideas that they think they might use.
If groups are having trouble thinking of ideas, you could try writing a list of suggestions on the board, but limiting groups to using one of your ideas only, to encourage them to think of their own. Some ideas could be:
- Favourite flavour of icecream/pizza/softdrink etc.
- Favourite pet
- Colour of eyes
- Shoe size
- Favourite vegetable
- Favourite type of music
Once groups have decided on their questions to ask, share them as a class, and ensure that they are all appropriate.
If groups need to change any of their questions, give them time to do so now.
Ensure that all groups record their questions for next session.
Data collection is a vital part of the investigation process. In this session students will collect data in tally charts for analysis in the following sessions.
Discuss with the class the best ways to collect the information from the class. Students may suggest asking the class and collecting the information in the same way as in Session 1. This will not be practical for the number of questions that need to be answered here.
Demonstrate how to draw a simple tally chart for others to answer questions on.
What is your favourite colour?
Show students how to mark a tally chart, with four vertical strokes for the first four marks and then a diagonal line to complete five.
Have each group construct three tally charts that clearly show their questions and give columns for the possible answers to be recorded in.
Place each group’s tally charts on a desk and have all groups rotate around the room until everyone has answered all the questions.
When groups are back at their own tally charts have them check that they can tell where all the tally marks have been drawn.
Have each group count the tallys in each category and write the number to save time in the next session.
In this session the students will work on creating bar graphs of the data collected in the previous session.
Show the graph created in Session 1 of numbers of siblings.
Discuss how it was made and what needs to be included on it.
Give students time to work on their first graph, providing support as required. Providing pre-drawn axes may be useful, but students may still need help selecting an appropriate scale to use on the y-axis.
After all students have completed one of their graphs bring the class together to share what students have done.
Discuss and compare graphs between groups.
Send students to work on the remainder of their graphs.
Session 5 is a finishing off session. Students should be given time to complete their graphs, and to write statements about what they show
Give groups time to finish graphs as required.
Students should also write statements under each graph telling what the graph shows. Starters for these statements could be given:
- The most popular…
- The least popular…
- Most students in our class…
Discuss with the students whether there is any action we should take as a result of any of the information we have found out in our investigations.
Ask if there are any conclusions we can make from the investigations we have done.
Students could compile their graphs as a booklet to take home to their families entitled "About our class" or similar. Alternatively, create a class display of the findings, or share them with another class.