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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.

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Elaboration on this Achievement Objective

This means that students will use the statistical enquiry cycle to plan and conduct investigations. The cycle has five phases that relate to each other. Some enquiries follow these phases in sequence but often new considerations mean that a statistician must go back to previous phases and rethink. The phases are:

 Statistical investigation cycle.

 
At Level Five students should be able to pose suitable questions for data driven inquiry. The questions may be:
  1. Summary, for example, what is the normal height of a 14-year-old female?
  2. Comparitive, for example, do males do more exercise than females?
  3. Relational, for example, is there a relationship between television watching and lack of exercise?
Given a question or assertion, students need to decide on appropriate variables, for example, age, gender or hours of TV viewing, to answer a question or interrogate an assertion. The choice of attribute leads to choices of measures for that attribute, for example measure exercise by both time in minutes and intensity using a 1-10 self-reported scale.
At Level Five students sophistication in data collection and analysis should extend to the need for representative sampling and adequate sample size, avoidance of bias in surveys and sampling techniques,  systematic collection and processing of data that does not narrow potential responses, and appropriate use of technology to sort and display data.
 
Students should use a variety of displays to find patterns or relationships in multivariate data sets. This range of displays should extend to using measures of centrality and spread such as mean or median, range and quartiles. This means that displays such as box and whisker plots and histograms are accessible.

Students should analyse the data by comparing distributions visually using multiple graph types, preferably generated by technology. They should use informal inference to look for differences between distributions, for example, the median of one group is higher than the upper quartile of the other. Students should choose the most appropriate data display to report their findings and draw conclusions from the data related to their investigative question. They should recognise that all findings from the analysis of samples must be interpreted with uncertainty and be cautious in generalizing the results to whole.

 

Teaching resources for this Achievement Objective
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Action and Reaction

Level Five
Integrated
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.

find mean, median, mode of data

construct a graph

interpret data on a graph

comapre different graphs and decide which shows the data most clearly

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A Preliminary Investigation of Reaction Times

Level Five
Statistics
Units of Work
This unit is based on the survey instrument and data used in the Census At School: New Zealand project. In this unit students will become familiar with the site, generate random samples of data, and compare data using box and whisker plots.
  • Identify questions that can be answered using statistical data.
  • Discuss the notion of ‘outlier’.
  • Draw box and whisker plots.
  • Compare data using box and whisker plots.
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Census At School

Level Five
Statistics
Units of Work
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.
  • 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 further300
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Claws!

Level Four
Level Five
Integrated
Figure It Out activities
This is a level 4 measurement and statistics activity from the Figure It Out theme series. A PDF of the student activity is included.

interpret a tide chart

measure in millimetre with a ruler

create a graph to show data

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Crunchy fruit and vegetables

Level Five
Statistics
Rich learning activities
The purpose of this activity is to engage the students in a practical investigation following the statistical enquiry cycle.
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Discrete data

Level Five
Statistics
Units of Work
In this unit as students investigate small amounts of discrete data, they look at how changes in data affect calculated statistics. Building on what they learn, students solve a problem in context from a set of given data.
  • Discuss features of small amounts of discrete data.
  • Compare features of sets of small amounts of discrete data.
  • Plan and conduct an investigation to ascertain information from a set of data.
  • Report the results of the investigation concisely and coherently.
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Dragging school bags around

Level Five
Statistics
Rich learning activities
The purpose of this activity is to engage students in an investigation following the statistical enquiry cycle.
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Guess the Mass

Level Four
Level Five
Integrated
Figure It Out activities
This is a level 5 statistics and level 4 number activity from the Figure It Out series. A PDF of the student activity is included.

construct a line graph

describe the data

construct a box and whisker graph

find quartiles and median of data set

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Have your Fill

Level Five
Integrated
Figure It Out activities
This is a level 5 statistics and number activity from the Figure It Out theme series. A PDF of the student activity is included.

create a graph using a spreadsheet

interpret pattern in a graph

find percentages of a total

 

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Just Average

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.

calculate averages from data sets

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Moving Survey

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out theme series. A PDF of the student activity is available.

fomd the median from a data set

fidn the mode from a data set

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Reach for the Sky

Level Five
Integrated
Figure It Out activities
This is a level 5 number and statistics activity from the Figure It Out theme series.

find percentages of decimal numbers

show data on a graph

calculate mean, mode, and median of data

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Rent or Buy?

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out theme series. A PDF of the student activity is available.

calculate mean, median, mode from data tables using  calculator

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Scrum Power

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out theme series.

find mean, mode, median, range of data sets

compare data sets and justify method of comparison

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Suspect on Foot

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.

create a scatter plot

interpret information from a scatter plot

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Testing Times

Level Four
Level Five
Statistics
Figure It Out activities
This is a level 4 and 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.

construct a stem and leaf graph

calculate mean, mode, median, and discuss the data spread

decide which graph best shows the data

interpret data from a graph

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The Numbers Don’t Lie

Level Five
Statistics
Units of Work
The purpose of this unit is for students to learn and apply ideas about 'sample' to population statistics. This is done alongside the collection of data during physical education (PE) lessons.
  • Demonstrate understanding of control variables.
  • Develop investigative questions.
  • Organise data using a spreadsheet.
  • Use technology (CODAP) to process data and produce graphs.
  • Produce dot plots and box and whisker plots
  • Analyse dot plots and box and whisker plots.
  • Understand and use the “median outside the300
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Time Use Survey

Level Five
Statistics
Units of Work
This unit gives survey experience by providing students with the opportunity to design, collect and analyse data on the use of their time.
  • 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 investigation or improvements to their300
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Walking Tall?

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series. A PDF of the student activity is included.

construct a bar graph on a computer

interpret data from a graph

evaluate a hypothesis from the data

plan an investigation

collect and display data

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What is a typical Year 8 student?

Level Five
Statistics
Units of Work
In this unit students construct, administer and analyse a survey to consider what constitutes 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.