In this unit students construct, administer and analyse a survey to consider what is a typical Year 8 student.

- plan an investigation
- choose and construct appropriate data displays
- discuss features of data displays using mean, median and mode and looking at the range
- where appropriate state implications from their investigation
- look at possible further investigations or improvements to their investigation

Surveys are increasingly important in modern life. Surveys such at the national census are important for government planning. Surveys of teenage smoking tell organisations such as ASH how successful their programmes are. Surveys of the performance of political parties help the government to see how their policies are working and enable predictions of who might form the next government. Clearly it is important to be able to design, collect and analyse these surveys to get information which is as accurate as possible. This unit concentrates on these three facets of surveys to produce information about the typical Year 8 student.

Big sheets of paper

Tape measures

investigation, limitations, outliers, analysis, summary table, multivariate table, commonality

#### Prior to this Unit

It would be helpful if students were already familiar with some statistical ideas:

- Mean
- Mode
- Median
- Data displays
- Bar graphs
- Pie graphs
- Stem and leaf plots
- Histograms
- Range

#### Session 1

In this session students start to pose questions/develop ideas to help them find out what is a typical Year 8 student. (Reference is to Year 8 students but should be changed for the appropriate year level.)

- We have been asked to describe a typical Year 8 student.
*What sorts of things would we need to know to be able to describe a typical Year 8 student?* - Get students to brainstorm all of their ideas. Some starter ideas could be
- Physical attributes – hair and eye colour; height, arm span, length of legs, arms, gender
- Interests and hobbies – what sports they play, how much time spent watching TV, time on other activities, cultural and other activities …
- Related to school – time spent on homework, what is their favourite subject (avoid topics that may be upsetting to some students, especially weight).
- In groups get students to predict what they think a typical Year 8 student might be like using the main categories they have brainstormed above.
- Discuss how they will find out what a typical Year 8 student is like.
*What data will they need to collect?*

Who will they collect the data from?

How do they know that their sample is representative of all Year 8 students? (In their school? In their city/town? In NZ?) - Discuss practical matters.
*Which attributes and information should be collected in order to describe a typical Year 8 student?*

Will they survey their class only or do they need to survey other classes as well (this requires some organisation with other teachers – or other schools).

How will the data be collected?

How will the data be analysed? (Histograms? Mean? Etc.)

What might be the limitations of the data they collect?

How will they deal with outliers?

#### Session 2

In this session students are preparing for and then collecting data.

- Set up data cards to use to collect data. An example is below.
Name (optional): Gender: Age (years): Birth month: Colour of eyes: Colour of hair: Left or right handed: Length of right foot (cm): Height (cm): Armspan (cm): Sports played: Hobbies: Hours spent watching TV last week: Etc. - The rest of this session will be spent completing the data cards and collating the information into some sort of summary table. This will most probably be a multivariate table (use excel or paper version). An example is below.
Note 1: You might want to warn the students ahead of time so that they can collect accurate data on things like the number of hours of TV watched in a week.

Note 2: You might want to let the students work in pairs so that they can measure each others height, etc.

Name | Gender | Age | Birth month | Colour of eyes | Colour of hair | Left/ right hand | Length of right foot | Height | Arm span | Sports played | Hobbies Hours of TV |

#### Session 3/4

In this session students collate and reclassify the data in order to start to develop ideas about what a typical year 8 student is.

- Split students up into groups or pairs to explore different parts of the picture.

They may work on one particular area, for example ‘interests and hobbies’. They will first need to decide what features they want to look at, what would be appropriate displays to use and what statistics they might need to calculate. For example, if they ask what sports are played they can describe the number of sports played and then the types of sports played from this question. It would be appropriate to give some average for the number of sports (mean or median), it could also be appropriate to compare this with the mode.

They might also think about how outliers should be treated.

They might also explore the people who play two or more sports and see if there is a commonality amongst them.

It might be that if they are a boy and play two or more sports it is likely that one of the sports is soccer or if they are a girl and play two or more sports it is likely that one of the sports is netball. - Students should clarify what question(s) they are trying to answer, draw appropriate displays and then answer their question(s) showing some insight/depth in their response.

Going back to the sports example, it is not sufficient to say that a typical Year 8 student plays two sports, it is better to go into more detail about what those sports might be and how it might differ for boys and girls. - Students will need to present their results to the class and it would be good to have these on big pieces of paper to put up around the room.
- Get the students to pull together a number of ideas from the class results and try to draw a picture to represent a typical Year 8 student.
- Now that we have done all of this, what questions do we still have?
*Is there information that we now need that we didn’t realise we needed when we started?*

Could we have asked for different information that would have given us a better picture?

Would students in another part of the country have produced the same results?

#### Session 5

In this session students consider what a typical student at another year level would be like.

- If they are in Year 8 then it would be good to discuss how a Year 7 student might differ or be the same?

Then discuss how a Year 9 student might be the same or differ?*How confident are you on your ideas about Year 7? (Given that they have already been in Year 7)?*

How confident are you on your ideas about Year 9? (Given that they have not yet been in Year 9)? - Pick one or two attributes that they want to explore the differences/similarities between levels. If it is possible see if you can survey the other year levels and make comparisons.