Is there a difference?

Students need to experience many examples to develop their intuitions about whether the differences between data sets are meaningful. It is important to discuss why this is so.

The following plots show four pairs of data sets. Each pair represents the monthly rainfall data for 56 years for the months of January and September for an Australian capital. Each is accompanied by an intuitive comment on the population difference in rainfall.

 

Two dot plots, all data for September bunched near 0 mm, data for January spread fairly evenly from about 130 mm to 940 mm.

Monthly rainfall in September and January for Darwin.

 

You can be very confident in claiming that there is a difference in the rainfall between September and January in Darwin.

 

Two dot plots, all values for September spread fairly evenly from 10 mm to 170 mm, most data for January bunched at less than 30 mm with 4 values between about 46 mm and 102 mm.

Monthly rainfall in September and January for Perth.

 

You can also be very confident in claiming that generally there is more rain in September than in January in Perth.

 

Two dot plots, values for September spread from about 12 mm to 114 mm but more values less than about 77 mm, values for January positively skewed from 0 mm to about 62 mm.

Monthly rainfall in September and January for Adelaide.

 

Although there is considerable overlap, you can be quite confident in claiming that Adelaide has more rain in September than in January.

 

Two dot plots with very similar shapes, ranging from near 0 mm to about 150 mm for September, and from near 0 mm about 218 mm for January, the central part of each plot between about 30 mm and 75 mm.

Monthly rainfall in September and January for Canberra.

 

You cannot make any strong claims about the difference in rainfall for September and January in Canberra.

Some teaching advice on meaningful differences and an activity on differences in heights are provided.


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Curriculum links

Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)

ACMSP228

Source

Australian Curriculum, Assessment and Reporting Authority (ACARA)