Planning tool

Students:

• can analyse real-world data and summary statistics from reports and summaries available in media
• question the method of data collection and the inferences drawn from the reported analysis
• assess how the mean and median values were obtained from sampled datasets and which is the best measure of centre for the relevant data
• recognise the importance of statistics in today’s world, particularly on issues relevant to them.

Some students may:

• have trouble finding or selecting datasets independently and require further guidance.
• not question whether the report has used an appropriate dataset to support its claims.
• underestimate whether claims in opinion-based reports have used data out of context, wrongly or inadequately, or have used data that misrepresents the sample set.
• not question whether a data display in a report that has been derived from a particular dataset is the most appropriate display.
• underappreciate misleading claims, whether conclusions are ‘too good to be true’, whether uncertainty is acknowledged and whether enough information was used to support inferences and claims reported.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention

• We are learning to collect a valid sample of flights in and out of Australia on a given day.
• Using the sample, we are learning to make inferences about the population.

Why are we learning about this?

When an exact measurement seems difficult to attain for a particular question that we want an answer to, the best place to start is gathering a smaller amount of data. As we grow our dataset, we can look carefully for patterns or trends. These are clues that will lead us closer to the answer we seek in the most efficient way. This method can be applied in a vast array of settings.

What to do

You are going to determine the typical number of aircraft flying over an Australian state or territory. First you will need some data. I know what you’re thinking, this statistic probably exists somewhere online, but I want you to answer this question by collecting your own data. 

1. Acquaint yourself with one of the publicly available flight tracking websites or apps. These sites allow you to see flights happening 10,000 m above our heads. Experiment with the real-time maps. You should see something like this. 
    
2. We need to count the flights, but there might be too many, so select a small area centred around the place where you live.
3. Take a screenshot.
4. Determine how many planes are above you right now by simply counting them.
5. Next we need to find the typical number of planes that fly above you because we need to find measures of central tendency. Is right now a typical time?
6. To do this, let’s use systematic sampling. Determine a rule for how often you will collect one these screenshots. Follow your rule for 24 hours (or longer) and organise your findings in a table.
7. Use your data to calculate the measures of central tendency for your sample.
8. Compare your results to data you can find online. Do you think your sample mean and median are close to actual figures?
9. Assess the accuracy of your data. Did you take screenshots at appropriate times of the day? Did you miss the morning and evening rushes? Would things have been different on other days of the week?

Success criteria

• I can use systematic sampling to collect sample data for the number of aircraft over Australia or where I live.
• I can make inferences about the population from my sample.