Critical thinking about average
This task assesses students' levels of understanding of the mean.
To get the average number of children per family in a town, a teacher counted the total number of children. She then divided by 50 as there were 50 families. The average number of children per family was 2.2.
Which of these is certain to be true?
(a) Half of the families in the town have more than 2 children.
(b) More families in the town have 3 children than have 2 children.
(c) There is a total of 110 children in the town.
(d) There are 2.2 children in the town for every adult.
(e) The most common number of children in a family is 2.
(f) None of the above.
To use as an open-ended enquiry, students are asked to justify their rejection of the incorrect answers, as well as the choice of the correct answer (i.e. more than just choosing it).
It might be worded as follows.
Provide a mathematical justification for your choice of the correct answer. Then provide two answers demonstrating why the other alternatives are not certain to be true (i.e. one example where the claim is true and one where it is false).
You can download the Average Task: Possible Answers.