# 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

The statistical enquiry 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:

At Level Three students should be able to pose questions that they want to investigate, consider the appropriate data they need to collect, gather and sort the data in order to develop an answer to their question. The data involved should be multivariate so it should include many variables, for example gender, age, height, eye colour, bedtime, etc., so that relationships between the variables can be explored. Students should be able to ask summary questions (of a variable), for example what is the usual range in height for 10-year-old students?, comparison questions, for example are girls taller than boys?, and relationship questions, for example do older students go to bed later than younger students? Data displays, including tables and graphs, expected at Level Three are tally charts, frequency tables, pictographs, bar graphs, strip graphs, and pie charts for category data, dot plots and stem and leaf graphs for whole-number data, and simple line graphs for time series data. Students should be able to use computer technology to create these displays to find patterns, including trends over time, in data as well as to communicate their findings to others. They should be able to justify their choice of display/s with reference to the patterns they wish to highlight.

conduct a survey

collate survey data

create a graph

interpret findings

interpret information from a graph

write an investigative question

collect and collate data

display data on a graph

make conclusions

decide which graph is most suitable to represent the data

answer questions from a table

collect and display data

compare data groups and make conclusions

Students will:

- gather and record category data and investigate features of the data
- interpret data displays and draw conclusions from graphs.

Students should discover that:

- there is only a weak relationship between volume, mass, or product type and how it is packaged.

- display collected data in an appropriate format
- produce bar charts of data using Microsoft Excel
- make statements about implications or possible events based on selected data

categorise data

calculate percentages

construct a graph

make a conclusion from the data

construct a time-series graph using a computer

evaluate statements made about the data

interpret data shown on a pie graph

show fractions on a pie graph

find all possible outcomes

Students will:

- gather data on how long it takes for various items to decompose
- represent data on a timeline
- draw conclusions from data.

Students should discover that:

- patterns can be found in data
- these patterns have meaning.

Students will:

- measure, record, and average data for 2 variables (number of marbles and bungy cord stretch)
- plot a scatter graph using appropriate scales (independent variable on x-axis [number of marbles]; dependent variable [overall length] on y-axis)
- use tables and graphs to identify patterns/300

measure distances

measure times

record data on a graph

interpret patterns from the graph

- Plan a statistical investigation using the PPDAC cycle.
- Choose an appropriate data display (bar graph, dot plot, time series graph).
- Make statements about the findings of the investigation.

write investigative questions

make a conclusion

interpret statements made about a tally chart

discuss what information the stacked bar graph bests shows

pose questions for further investigation

construct a time-series graph

answer questions from graphs

make conclusions from own investigation

Students will:

- read a linear scale on a thermometer and record temperatures
- plot 3 series on a time-series graph.

Students should discover that:

- the slope of the graph (which represents the rate of change) is different for each tin
- temperature change is proportional to volume (the larger a volume of300

- Recognise what the variables are in a secondary data set.
- Sort the given data into categories.
- Answer investigative questions by sorting, organising and arranging data.
- Make sensible statements about the data with supporting evidence.

construct a tally chart

construct a bar graph

describe the features of a data set

write investigative questions