# Statistical Investigations: Level 4

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The key idea of statistical investigations at level 4 is telling the class story in detail with supporting evidence.

Students are building on the ideas from level three about different aspects of the PPDAC (Problem, Plan, Data, Analysis, Conclusion) cycle.  Key transitions at this level include posing comparison and relationship investigative questions, planning investigations including data generation, collecting and displaying measurement data, and comparing distributions visually.

Comparison and relationship investigative questions will be posed and explored.  Comparison investigative questions need to be about the group of interest and have an aggregate focus.  For example, do the boys in our class tend to be taller than the girls in our class?  Is there a relationship between armspan length and height for the students in our class?

Students should be planning to collect their own data for the investigative question they have posed.  This includes determining appropriate variables and data collection methods.  For example, they need to realise that to answer the first question they will need to measure student’s heights.  Along with this they will need to think about what units to measure with and whether students should leave their shoes on or not, and who will take the measures. This is data generation.

Students should be using dot plots and scatter plots to display data.  When comparing dot plot distributions visually they can identify the middle group by circling it and reason about the placement of the middle groups (shift) relative to one another.   They can compare (approximate) centres and the variation of the data in the middle groups.  Students can use tools such as hat plots and any statistical software that is available.  For scatterplots students should be looking at features such as the trend of the data points and how close the points are to the trend.  Adding a third variable, for example gender, by using colour allows for further exploration.

Students should be writing statistically sound statements about what their displays show.  The starter “I notice...” is a useful way to encourage students to write about what their displays show.  In addition students should be encouraged to write “I wonder...” statements for further investigation.

This key idea develops from the key idea of statistical investigations at level 3 where students are telling the class story with supporting evidence.

This key idea is extended in the key idea of statistical investigations at level 5 where students are telling a story about the wider universe with supporting evidence.