Go out and collect a modest-sized, discrete dataset. Name lengths of all of the students in your classroom, say, or the number of people in each of their households.
This bar graph is only tangentially relevant, being more of a case-value plot of four different populations. But it breaks up a texty post. So deal with it.
Now play with that data.
If we add one or more new (hypothetical) cases, can we…
- Increase both the median and the mean?
- Decrease both the median and the mean?
- Increase the mean while decreasing the median?
- Vice versa?
- Increase the Mean Absolute Deviation (MAD) while decreasing the mean?
- Vice versa?
- Decrease both the MAD and the range?
- Decrease the MAD while increasing the range?
- Vice versa?
If we delete one or more actual cases, can we…
- [same list as before]
Thanks to Susan Friel, Connected Mathematics and tons of other creative folks for getting me started with this. Future elementary teachers to tackle this shortly. I’ll report back.
Overthinking my teaching 