My Bongard problem n.17. I'm trying to change topics more. Try to write your solution (with a spoiler if you want), and to spot any mistakes of mine. I'll give my solution to this problem... Monday.

For more info about Bongard problems in general take a look at my first messages:
https://mathstodon.xyz/@leonardom/116110015131667314
https://mathstodon.xyz/@leonardom/116110093951382315

#bongardproblem #mathpuzzle #puzzle #visualmath

It's about statistics :-)
@leonardom That's the obvious part 🙃

Unlike most others, in this Bongard problem the boxes on the left are approximately paired with the right ones to make it simpler to find (to see) the solution. The boxes appear to contain some random 1D distributions (on the other axis they are always uniformly scattered). The distributions have slightly different densities from left to right, but they seem the same or very similar. And the cursors seem to point to some measure of central tendency. But the cursors are in slightly different positions between the two sides, consistently. Once you remember one of the first images in statistics books, you're done.

https://en.wikipedia.org/wiki/File:Visualisation_mode_median_mean.svg

Solution to my BP n.17: In the left boxes the cursor at the base points approximately at the medians of the distributions. While in the right boxes they point to their mean.

Detailed contents of each box:
1: Uniform distribution;
2: Gaussian distribution centred in the middle of the box and with sigma=20;
3: Triangular distribution, the mean is shifted 26 pixels on the right of middle of the box;
4: Exponential distribution with lambda=0.03;
5: Gamma distribution with alpha=6.0 and beta=6.0;
6: (empty);
- - - -
7: distribution like box 1;
8: distribution like box 2;
9: distribution like box 3;
10: distribution like box 4;
11: distribution like box 5;
12: (empty).

All of them are famous distributions. In each box I've plotted about 1000-2000 dots, but the amount varies between boxes. I've generated the boxes using small Python programs using the real-valued-distributions of the Python standard library and the Pillow library. Means and medians found analytically where possible, numerically otherwise.

#bongardproblem #mathpuzzle #puzzle #visualmath

File:Visualisation mode median mean.svg - Wikipedia