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Planning a Statistics Investigation L3

Purpose: 

In this unit students will identify how to plan and carry out a statistical investigation, looking at using comparisons, controls and measurable data.

Achievement Objectives:

Achievement Objective: S3-1: Conduct investigations using the statistical enquiry cycle: gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions; identifying patterns and trends in context, within and between data sets; communicating findings, using data displays.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  • 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.
Description of mathematics: 

It is vital when planning statistical investigations that the students understand the importance of the way that they 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. Throughout this unit the students will first look at choosing a topic to investigate, making sure that the topic lends itself to being investigated statistically. They will then look at a variety of ways of collecting their data and the best way to record it. Once they have collected and recorded their data they will then investigate the best way to present their findings, taking into consideration the needs of their intended audience. To evaluate the investigations there can be a combination of methods used, depending on the students, the topics and the intended audience. It could be useful for the students to send their completed investigations and findings to concerned parties for more realistic feedback.

Required Resource Materials: 
Magazines, newspapers etc containing relevant examples of different types of graphs that can be used to present statistical data
Presentation materials
Key Vocabulary: 

 investigation, purpose, validity, questionnaires, measurable, evaluation, sample size, constructive feedback

Activity: 

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

Session 1 provides an introduction to statistical investigations. The teacher will need to provide the students with plenty of magazines and newspapers that have some good examples of how data can be presented effectively and also perhaps some examples of poorly displayed data. Ask the students to spend some time at home looking through magazines and newspapers to find positive examples.

  1. Start the session with a class discussion to get the students thinking about whether or not we have a need for statistical investigations, and who uses the information?
    What is a statistical investigation?
    Can you think of an example when we might need to carry out a statistical investigation?

  2. Organise the students into groups of 2 or 3. Give out magazines and newspapers and ask the students to find some examples of statistics.

  3. Ask the students to look closely at the examples they have selected. Ask them to consider the following questions;
    Who has done the research for/carried out this investigation?
    Who will benefit from the results of this investigation?
    Is it clear to you what the purpose of the investigation is?
    What do you like about the way that the information is presented?
    Does it help you in any way to understand the information better?

Do you think the information could have been presented in a different way to help the audience understand the findings? If so, what would have made it better?

  1. Class discussion to share ideas from each group. Have the students all come up with the same ideas? Try and steer the students towards the conclusion that the best way to present the information depends on the information itself. For example there would be no point in displaying class members’ heights on a pie graph.

Session 2

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.

  1. Recap the discussion from the previous day about the purpose of an investigation and make sure the students know to choose a topic that will have some benefit or serve a purpose.

  2. Provide the students with a list of topics to choose from, or suggest that they might like to come up with their own topic, eg. How tall are students in our class? How many cars drive past our school?

  3. Teachers will need to ensure that topics are realistic to investigate especially in the given time frame.

  4. Working in groups students select a topic and decide what the main question is that they want to answer. ie What is the purpose of their investigation?

Session 3

Data collection is a vital part of the investigation process. The teacher will need to stress to the students once again, the importance of being consistent in the collection of their data. There will be a need also for discussion to take place about efficient ways to record data. Some students may need a fair amount of assistance in recording their data.

  1. Introduction to the session covering the different ways to record data eg tables, tally charts, questionnaires, etc.

  2. Students should be given time to organise and prepare their chosen method of data collection. eg. If they have chosen a questionnaire, they should ensure it is complete, or if they are going to count cars passing the school, they should set up a tally chart ready to use.

  3. Students need to check with the teacher before commencing data collection to ensure that their method of collection is the most appropriate.

  4. Students to spend time collecting their data and recording it efficiently, stopping at various stages to talk about the points covered in session 1.

Session 4

In this session the students will be looking at data analysis and deciding which way would be best to present information. The students will need to look at a variety of examples before they even begin to select their presentation format. The focus should be on choosing the most clearly understandable information. Some groups make take a lot longer to agree on a format.

  1. Small group discussion about the best way to present the information, providing some examples from previous years or other investigations from magazines etc.

  2. Come together as a class and share ideas from small groups about how we can present information eg graphs, charts, summary conclusions etc.

  3. Discuss the different ways to convert data so that it can be graphed eg percentage into pie graph etc.

  4. It would be a good idea at this stage to revise how to create various graphs, looking specifically at the features of graphs such as

    1. Title

    2. Axes – labelled

    3. Scale

    4. Key

  5. Use this time to start presenting information into graphs, tables or any other format.

Session 5

Session 5 will focus on the final presentation of the data each group has found out. Encourage the students to be constantly evaluating what they are doing. Explain that it is fine to discover that a particular way of presentation is not working, and that it is a good idea to make adjustments.

  1. Use this time to finish presenting information in graphs, tables or any other format.

  2. Present information in a way that includes the important parts of their investigation.

    1. Topic chosen

    2. Survey/Questionnaire
    3. Sample size
    4. Collection of data
    5. Results – tables/graphs
  3. Once groups have finished presenting their information they will be required to make a concluding statement that links directly with the original question they asked in session 2. ie what did you discover?
  4. In groups, the students will share finished information with the class.

  5. Evaluation: (Peer and Teacher)
    1. Give feedback, including constructive criticism.
    2. Is the information easy to understand?
    3. Could we make it any clearer?

  6. Talk about who could use the information that has been presented. Can we send it to anyone outside school? For example investigations related to a road safety issue could be forwarded to the local council.