This is a nice little starter for students to look at life expectancies using random and representative sampling. They should get very different answers (using both methods and from each other).
Instructions for the Students:
A Slice of Life: Sampling Life Expectancies
The data is shown below that the students used is on one side of the worksheet which can be downloaded below:
Instructions for the Students:
A Slice of Life: Sampling Life Expectancies
 On the other side of this worksheet (or the next page) is a pictogram showing the life expectancy rates for a selection of countries. This selection represents all the major global regions and includes countries which are rated by the UN as being at either high, medium or low levels of development.
 Each of the 40 countries is represented by its national flag, which is accompanied by the life expectancy rate in country.
 Your task is, firstly, to calculate the mean average of the forty countries' life expectancy rates, by taking a random sample of 10 countries.
 Select 10 countries at random and then add their life expectancies together than then divide by 10 (the number of countries you used in your sample)
 We will feed back results to the class
 Next calculate the mean average of the forty countries' life expectancy rates, by taking a representative sample of 10 countries.
 Select 10 countries so that you have a mix of high, medium or low levels of development and then add their life expectancies together than then divide by 10 (the number of countries you used in this sample)
 The true mean of the 40 countries' life expectancies will also be revealed.
The data is shown below that the students used is on one side of the worksheet which can be downloaded below:
The students do the calculations and then complete the table before the teacher reveals the actual answers  then class dicussion can centre around why there were differences  this then leads to further discussion of sampling techniques.

