Planning tool

Students:

• analyse and report on different distributions of data that may have been derived from primary or secondary sources
• investigate a variety of different sampling procedures and recognise these methods as random or non-random methods of collection
• expand their vocabulary to include terms such as 'sample distribution' and 'sample space'.

Some students may:

• not realise that a sample size from a large population is used to make generalisations about the population.
• not understand that two different samples from the same population may show variable results.
• underestimate the differences between very small samples sizes versus very large samples sizes.
• underestimate the affect of bias samples.

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

• I am learning about sampling techniques and the effects on the reliability of statistics.
• I will use several methods to create samples and compare statistics.

Why are we learning about this?

We need to be very aware when looking at data that we are given the whole picture. The way in which a sample is collected and displayed has a significant influence on possible decisions to be made.

What to do

A lolly manufacturer employee weighs a sample of all the lollies made each hour to make sure the correct weight is being produced.

A sample of 10 lollies is taken and statistics are calculated.

Management wants to ensure that the samples are an accurate representation of all the lollies produced. Not only does the advertised weight of each lolly bag have to be accurate so that customers don't complain, but also because sometimes bags of lollies weigh a little more or a little less. The manufacturer wants to make sure that they don't give away the product! The results are recorded in the table below.  

What you are going to do is to generate random samples each with 10 pieces of data using different methods.  

Sample 1: Random sampling

1. Roll a 10-sided dice to choose the location of random pieces of data from the table. The piece of data selected will be located by row and column. The first roll will determine the row, the second roll the column. For example, a roll of 3 then 8 would result in the piece of data in the third row and eighth column (8.4).
2. There are no repeats, so roll again if the same location on the table is rolled, until 10 pieces of data are collected.
3. Collect 5 pieces of data using random sampling.
4. Collect 20 pieces of data using random sampling.

Sample 2: Convenience

1. Select the first 10 pieces of data, in the first column, off the production line.
2. Select the first 5 pieces of data, in the first column, off the production line.
3. Select the first 20 pieces of data, in the first two columns, off the production line.

Sample 3: Systematic

1. Roll the dice twice as you did in Sample 1: Random sampling. Select every third piece of data until 10 pieces of data are collected.
2. Roll the dice to choose a random starting place and select every fifth piece of data until 10 pieces of data are collected.
3. Roll the dice to choose a random starting place and then select every seventh piece of data until 10 pieces of data are collected.

Analysis questions

1. For each sample generated, calculate the mean, median and range.
2. What would you report to management about the lollies produced and the most practical, and accurate, way to generate samples?
3. Challenge: If management require a serving size (individual lolly) to be 7.2 grams, does the production line need to be adjusted to meet the weight requirements?

Success criteria

• I can use different sampling techniques to generate a sample from a population of data.
• I can compare statistics from samples to evaluate the effect on the reliability of the statistics.