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Back to CensusAtSchool home page CaSMa11 - Environmental Graphs


You can download this activity, the teacher solutions and the assessment rubric as a rich text file (RTF) at the bottom of the page. Download our printer friendly Prepared Samples as Excel files or access data using the Random Sampler.



Subject Area

Mathematics




Key Statistical Literacy Competencies Addressed
  • Data awareness
  • The ability to understand statistical concepts
  • The ability to analyse, interpret and evaluate statistical information
  • Communicating statistical information and understandings


Overview
This lesson introduces the concept of deviation from the mean. Students compare the environmental issues summary data for each state. They use each State and Territories Environmental mean to calculate how issues in each state deviate from this mean.



Requirements
  • Calculator
  • Student Worksheet


Instructions


Environmental Graphs

CensusAtSchool Environmental Opinion Results for States and Territories

The summary statistics for the 2010 CensusAtSchool questionnaire showed the following results on the importance for six Environmental Opinion Issues, where a rating of 0 represented Not Important and 999 represented Very Important:

IssueACT NSWNTQLDSATASVICWAIssue overall mean
Reducing pollution713.4 694.6679.2652.6655.2621.7680.3685.9
Recycling our rubbish721.2 685.8641.2628.3638.0615.4673.9651.3
Conserving water768.4 722.2672.6690.0723.3625.1752.1712.0
Reducing energy usage681.3 647.8623.6615.5597.5563.6635.5630.5
Conserving old growth forests635.2 585.2616.5580.0552.8558.3568.3587.8
Protecting coastal/marine environments702.7 672.9672.8668.2632.5635.3646.5667.1
State/Territory Overall mean


1. In the last row calculate the overall State and Territory mean to one decimal place.

2. Use the overall State and Territory mean to make a column graph on the axes below.

Graph - environmental issues mean ranking by state and territory

3. Comment on the results

4. In the last column of the table calculate the overall issues mean to one decimal place.

5. Use the axes below to make an overall Environmental Issues mean column graph.

Graph - 2010 summary environment issue

6. Comment on the results


The Mean as a measure of the Centre of Data

As the mean is one measure of the centre of data you can check that your results look reasonable by counting the number of values above and below each mean. They should be roughly even.

7. Fill in the table below to show how the ratings varied from the State/Territory overall mean.

State/ TerritoryACTNSWNTQLDSATASVICWA
No. above the mean
No. below the mean
8. Were the results even for all States and Territories? If not, can you suggest a reason?
For example, the Queensland mean environmental rating is 639; there are three issues that scored higher than this and three that scored lower.


The Deviation from the Mean

If the mean is the centre of the spread then how far each value is from the mean gives an indication of how each variable is perceived. This difference from the mean is known as the deviation from the mean. A positive deviation means that a value was ranked above the mean while a negative value means that it was ranked below the mean. The deviation from the mean is calculated by subtracting the mean from the value. This is written mathematically as

deviation from the mean = x –

where x is the score or value and (called x bar) is the mean.
E.g. 1 In Victoria, for conserving water: deviation = 752 – 659 = 93
This means that conserving water is quite a bit higher in ranking than the overall mean.
E.g. 2 In Queensland, for conserving old growth forests:
deviation = 580 – 639 = 59
This means that conserving old growth forests is lower in ranking than the overall mean.

The graphs on the next two pages use each deviation from the mean to show the importance that students from each State and Territory placed on the six Environmental issues.

9. Use the graphs and the table above if necessary to answer true or false to the questions below. Where you answer false, give the correct response.

STATEMENTTRUEFALSE
ANSW and Tasmania were the only States/Territories where four issues rated above the mean and two below.
BConserving water scored the highest positive deviation in each State and Territory
CConserving old growth forests had the highest negative deviation from the mean in all States and Territories.
DConserving water in Victoria had a higher deviation from the mean than in SA.
EIn all States and Territories reducing pollution ranked more highly than recycling our rubbish
FRecycling our rubbish had a positive deviation in all States and Territories.
GReducing energy and protecting old growth forests had a negative deviation in all States and Territories
HTo say that an issue had a negative deviation is the same as saying it was ranked below the overall mean.
IReducing energy ranked highly in all States and Territories
JResponses in NT were clustered closest to the mean compared to the other States and Territories


10. You should have found 4 FALSE statements. Correct them by writing a TRUE statement below.
(i)

(ii)

(iii)

(iv)

ACT Environmental Issue Graph

NSW Environmental Issue Graph

NT Environmental Issue Graph

QLD Environmental Issue Graph
SA Environmental Issue Graph

TAS Environmental Issue Graph
VIC Environmental Issue Graph

WA Environmental Issue Graph




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Student Worksheet




Teacher Solutions






Assessment Rubric










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