High School Can you pick out the random set of points in a plane?

[Spinnor]

TL;DR

Can you pick out the random set of points in a plane?

The above screen shot is from, @ the 1:43 mark. Which set of points is random? Answer below.
The right set of points.

 

[Dale]

Did that surprise you? The one on the left is far too even to be "random".

Of course, I am assuming that by "random" you mean that each point is placed at a location (X,Y) where X and Y are independent random variables each with a uniform distribution. You could have random X, Y that are not independent but are nevertheless random or you could have random X, Y that are not uniformly distributed.

 

[Spinnor]

Did that surprise you?

I stopped the video to think about the pictures. I guessed right. The picture on the left is by some measure random as explained in the video. The answer might not be obvious to everyone. Thought some here might enjoy it.

 

[FactChecker]

The picture on the left is by some measure random as explained in the video.

I disagree. The video is using the term "random" to mean "random and independent of each other". As the video says, those points start out random, but then criteria are applied based on the prior dots to determine if each new dot will be included or not. So the dots are not independent of each other.

The answer might not be obvious to everyone.

It certainly is not. There is more clustering in random independent events than people expect in general. When they see a random cluster, they very often think that something non-random is going on. For instance, a baseball batter on a hitting streak is often thought to be better in general. But it might just be the clustering of random hits.

Thought some here might enjoy it.

I think that it illustrates a good point.

 

[Spinnor]

For instance, a baseball batter on a hitting streak is often thought to be better in general.

As far as hitting baseballs I am pretty sure that in addition to some randomness and fluctuations in the pitcher's pitches, a batter can peak both physically and mentally and be better able to hit a homer so a streak of home runs can be the result of both random and non random conditions? Same goes for the pitcher, his abilities can peak and make it harder for the home run hitter?

 

[FactChecker]

As far as hitting baseballs I am pretty sure that in addition to some randomness and fluctuations in the pitcher's pitches, a batter can peak both physically and mentally and be better able to hit a homer so a streak of home runs can be the result of both random and non random conditions? Same goes for the pitcher, his abilities can peak and make it harder for the home run hitter?

Sure. That is why I said that the hot streak might just be a random cluster of hits. But, IMHO, people tend to underestimate the amount of clustering in independent random events. Therefore, they tend to attribute a hot streak to physical and mental ability more often than they should.

 

[Ibix]

But, IMHO, people tend to underestimate the amount of clustering in independent random events.

There was an article I read years ago, in the Royal Statistical Society magazine I think, talking about accident blackspots. They were defined as places on the roads where more than five accidents had happened in the preceding year, and are marked as dangerous by road signage. Fine. But they've kept the definition, so any time a place has more than five accidents in a year it gets classified as an accident black spot. The article was pointing out that everywhere will eventually have five accidents in a year just by bad luck. Apparently this kind of clustering-by-chance escaped whoever framed the definition.