Central tendency mean activity1

Activity - Discussion - when is mean useful and when it is not

Estimated Time

Half period

Materials/ Resources needed

Illustration - Consider the wages of staff at a factory below:

Staff	1	2	3	4	5	6	7	8	9	10
Salary	15k	18k	16k	14k	15k	15k	12k	17k	90k	95k

Is the mean a good measure of central tendency for the data given above

Prerequisites/Instructions, if any

None

Website interactives/ links/ simulations/ Geogebra Applets

1. https://en.wikipedia.org/wiki/Arithmetic_mean
2. https://explorable.com/arithmetic-mean
3. http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Arithmetic_mean.html

Process (How to do the activity)

Share the example and ask students if the mean has been a good measure for central tendency

Developmental Questions (What discussion questions)

The mean salary for these ten staff is 30.7k. However, inspecting the raw data suggests that this mean value might not be the best way to accurately reflect the typical salary of a worker, as most workers have salaries in the $12k to 18k range. The mean is being skewed by the two large salaries. Therefore, in this situation we would like to have a better measure of central tendency. As we will find out later, taking the median would be a better measure of central tendency in this situation.

Evaluation (Questions for assessment of the child)

1. Is the mean a good way to measure the average income of a citizen (per capita income)
2. In what way do outliers make mean a measure that is not robust

Activity Keywords

To link back to the concept page central tendency