Census At School

Purpose

This unit develops statistical literacy exploring multivariate data sets that have been created by the students and from the CensusAtschool (NZ) and CensusAtschool (International) sites.

Achievement Objectives
S5-1: Plan and conduct surveys and experiments using the statistical enquiry cycle: determining appropriate variables and measures; considering sources of variation; gathering and cleaning data; using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets; comparing sample distributions visually, using measures of centre, spread, and proportion; presenting a report of findings.
Specific Learning Outcomes
• Plan an investigation including selecting an appropriate sample 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 investigation or improvements to their investigation.
Description of Mathematics

Most countries these days have regular censuses of their populations in order to plan for the future and to judge how well past planning has been. Censuses are not recent inventions by any means. You might know of two very famous ones. The reason that Mary and Joseph were going to their Bethlehem when Jesus was born was that the Emperor Augustus had ordered a Roman census of the Roman Empire. After William the Conqueror conquered England in 1066, he commissioned a census that was collected in what was called the Doomsday Book. The first complete draft was in 1085. So censuses are important tools for the efficient running of a country and have been for a long time. CensusAtSchool is an international project that enables students to learn how to organise the collection of data and to analyse that data. This unit aims to introduce students to CesusAtSchool.

Required Resource Materials
• Questionnaire from NZ CensusAtSchool site to complete (see session 1 for details)
• Questionnaire(s) from CensusAtSchool sites.
• Internet access
• Own version of CensusAtschool questionnaire
Activity

Prior to this Unit

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

• Mode
• Mean
• Median
• Data displays
• Bar graphs
• Pie graphs
• Stem and leaf graphs
• Histograms
• Random sample

Session 1 – Internet access is required for online exploration.

In this session students find out what a census is and look at the CensusAtSchool questionnaire . This session could be carried out as a whole class session using a data projector, in a computer lab with individuals (or small groups) using their own computers, or using printed resources downloaded from the internet prior to the lesson.

1. New Zealand Census – To explore this aspect go to www.stats.govt.nz/topic/census. This is the home page for the National Census.

Some starter questions to help explore the census information.
• What is a census?
• How often do we have them in New Zealand? When was the last one, when is the next one?
• Why do we have a census?
• What types of questions are asked?
• Who is covered by the census?
• When did New Zealand first do a census?
• What years did New Zealand abandon taking a census and why?
• Add any other questions that you think might be relevant for your class.

2. Find the CensusAtSchool site. www.censusatschool.org.nz Click to find out about New Zealand census at school project.
Key questions
• What is CensusAtSchool?
• How is it different from the New Zealand census?
Have a look at the questions used.

3. Print off the questionnaire used. Make a selection of the questions for students to complete (on paper) as they look at the survey. Some questions require that you be online, and will not be able to be used.

4. Collect these in and let the students collate the data to use it for comparison.

Sessions 2-5

Over the remaining sessions students explore the data collected in the class questionnaire and compare with the national results and international results.

CLASS DATA

1. Collate the class data into a multivariate table and give to the class.
Codes: Gender: M(male) F(female)
Height in centimetres
Length of foot in centimetres
Colour of eyes: Br(brown) B(blue) G(green) O(other)
Mobile, computer, internet, calculator: Y(yes) N(no)
Travel to school
W(walk) M(motor vehicle) B(bus) T(train or tram)
K(bike) S(skateboard) C(scooter) O(other) Favourite subject: record only 1st favourite Recommend first three letters to code.
 Gender Height Length of foot Colour of eyes Mobile Computer Internet Calculator Travel to school Minutes to get to school Favourite subject
2. Before students analyse the data get them to brainstorm questions they could ask of the data. They will probably start with straightforward category type questions, but see if you can get them to look at multi category questions?

Examples of straightforward category type questions
• What colour of eyes will be most common?
• What will be a representative height of the class?
• How will most people travel to school?
• What time do you think it takes most people to travel to school?
• What will be the most common favourite subject?
• How many people in the class do you think will have a computer at home?

Examples of multi category questions
• Do the people who walk to school take more time to get to school than the people who come by car?
• Do people who have a computer at home also have internet access?
• Who is more likely to have brown eyes, boys or girls?
Get them to predict what they think the class results will look like for the different questions.

3. Split the students into groups and get each group to take one of the questions posed by the class. They will need to draw a graph to display their data and then answer the question. It would be good for each group to have one straightforward category question to work with and one multi category question to work with. Part of the discussion will involve what type of graphs to draw for each of the different questions. Some of the questions may require regrouping of the data. This would be best done onto either OHT or large sheets of paper so it can be displayed and students can report back what they have found.

COMPARISON WITH NATIONAL – LIMITED QUESTIONS

1. From the CensusAtSchool site get the summary information from the summary tables. This is limited to overall results for gender, technology access, breakfast choices, favourite subject and travel time to school by region. This is enough for the students to be able to look at the class results and write comparison statements about how their class is different to the national statistics. It would be interesting for them to think about why their results might be different (if they are) to the national statistics.

SAMPLE VERSUS CENSUS

1. Now we want to compare the rest of our questions with the national results. Do we need to have all of the results in order to get a picture of what the national data might look like? If we do, how could we do that? How long would it take? How much would it cost? Is it something we could do easily?

2. Split the class into groups (or samples) of 5-6. Pick 3-4 of the questions from the ones posed earlier to work with, it might be easier to work with straightforward category questions at this stage.

In their group answer the questions and then compare this with the class results. Were their group results a good prediction of the class results? What is it about their group that makes it not suitable? (Friendship groups might be all one sex for example which would give a bias response for gender questions.) How could we split the class into groups to give a fairer representation? (Idea of randomness, names out of a hat, for example). Try doing this. Get these groups to look at results to questions and see if they better represent the class results. Try to develop the idea that a sample can provide representative information about the population if it is randomly selected. CensusAtSchool makes it easy to produce a randomly selected sample. Click "get a random sample" under the "data" heading. Filters include gender (mixed, male, female) region (North Island, South Island, New Zealand) and year level (5-10).

COMPARISON OF THEIR QUESTIONS WITH NATIONAL DATA

1. Discuss in class how they might go about comparing their results with the national results using a sample data set. What size should the data set be? The same size as the class for direct numerical comparison or a different size using proportional (percentage) comparisons. How big would be too big? Time to analyse and sort data within the time constraints. Should they all use the same sample to answer their different questions, or could they all make up their own sample of data from the CensusAtSchool site to use?

It may be worthwhile looking at a few different samples and looking at the results for a straightforward category question to see if they are similar or different.

2. Once the above decisions are made get the students to answer their questions for the national data. You may like to download the datasets yourself for the class or get them to go and download the datasets themselves. They can then organise the data in an Excel spreadsheet to get just the information they are interested in.

3. Once they have the national data information they can compare the class results with the national results.
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Level Five