Those are not the actual number of school shootings in the way people think of school shootings. 

I'm not the arbiter of what people think and neither are you.  If you are upset that news organizations record verifiable information to a different standard than you'd like, that is your problem, not mine.  I stand by my vetted figure but will gladly change it if a new standard dictates how information is reported.  Call it "18 separate incidents involving unlawful discharge of firearms on the property of education centres in America" if it really means so much to you.  My original context remains unchanged, and everything I've claimed has been independently verified.  

It's entirely arguable whether neanderthalensis and homo sapiens are considered to be separate species.  

Which is why some call them homo sapiens neanderthalensis.  

https://biology.stackexchange.com/questions/39664/how-could-humans-have-interbred-with-neanderthals-if-were-a-different-species

"Short answer

The concept of species is poorly defined and is often misleading. The concept of lineage is much more helpful. IMO, the only usefulness of this poorly defined concept that is the "species" is to have a common vocabulary for naming lineages.

Note that Homo neanderthalis is sometimes (although it is rare) called H. sapiens neanderthalisthough highlighting that some would consider neanderthals and modern humans as being part of the same species.

Long answer

Are neanderthals and modern humans really considered different species?

Often, yes they are considered as different species, neanderthals being called Homo neanderthalisand modern humans are being called Homo sapiens. However, some authors prefer to call neanderthals Homo sapiens neanderthalis and modern humans Homo sapiens sapiens, putting both lineages in the same species (but different subspecies).

How common were interbreeding between H. sapiens and H. neanderthalis

Please, have a look at @iayork's answer.

The rest of the post is here to highlight that whether you consider H. sapiens and H. neanderthalisto be the same species or not is mainly a matter of personal preference given that the concept of species is mainly arbitrary.

Short history of the concept of species

To my knowledge, the concept of species has first been used in the antiquity. At this time, most people viewed species as a fixed entities, unable to change through time and without within population variance (see Aristotle and Plato's thoughts). For some reason we stuck to this concept even though it sometimes appears to not be very useful.

Charles Darwin already understood that as he says in On the Origin of Species (see here)

Certainly no clear line of demarcation has as yet been drawn between species and sub-species- that is, the forms which in the opinion of some naturalists come very near to, but do not quite arrive at the rank of species; or, again, between sub-species and well-marked varieties, or between lesser varieties and individual differences. These differences blend into each other in an insensible series; and a series impresses the mind with the idea of an actual passage.

You might also want to have a look at the post Why are there species instead of a continuum of various animals?

Several definitions of species

There are several definitions of species that yield me once again to argue that we should rather forget about this concept and just use the term lineage and use accurate description of the reproductive barriers or genetic/functional divergence between lineage rather than using this made-up word that is "species".

I will below discuss the most commonly used definition (the one you cite) that is called the Biological species concept.

Problems with the definition you cite

A species is often defined as the largest group of organisms where two hybrids are capable of reproducing fertile offspring, typically using sexual reproduction.

Only applies to species that reproduce sexually

Of course, this definition only applies to lineages that use sexual reproduction. If we were to use this definition for asexual lineages, then every single individual would be its own species.

In practice

In general, everybody refers to this definition when talking about sexual lineages but IMO few people are correctly applying for practical reasons of communicating effectively.

How low the fitness of the hybrids need to be?

One has to arbitrarily define a limit of the minimal fitness (or maximal outbreeding depression) to get an accurate definition. Such boundary can be defined in absolute terms or in relative terms (relative to the fitness of the "parent lineages"). If, the hybrid has a fitness that is 100 times lower than any of the two parent lineages, then would you consider the two parent lineages to belong to the same species?"

http://www.slate.com/articles/news_and_politics/explainer/2010/05/pizzly_bears.html

I'm not the arbiter of what people think and neither are you.  If you are upset that news organizations record verifiable information to a different standard than you'd like, that is your problem, not mine.  I stand by my vetted figure but will gladly change it if a new standard dictates how information is reported.  Call it "18 separate incidents involving unlawful discharge of firearms on the property of education centres in America" if it really means so much to you.  My original context remains unchanged, and everything I've claimed has been independently verified.  

penguins have adapted wings, they do not have the same type of fins or flippers that dolphins or other aquatic animals have

"I don't think you'll find that he made the blanket assertion that there exist no groups into which animals can be sorted."

that is exactly what he said, go back and read his posts before you get involved and that is exactly why i responded in the way i did

is therefore, in my eyes, 

Your eyes are not the arbiter of the way things are and neither are mine. 

"If you are upset that news organizations record verifiable information to a different standard than you'd like, that is your problem, not mine.  I stand by my vetted figure but will gladly change it if a new standard dictates how information is reported."  --Literally a segment that you responded to.

I am guessing that you missed that important part, considering you relied on "your eyes" instead of a standard for reporting.

When I side with Aeolus against you—and I am—you ought to re-examine your position.  For one thing, the word "shoot" usually implies a target.  Therefore, it's a stretch IMO to call accidental weapon discharge that hurts nobody a "shooting".  To equate what you are now prepared to call "unlawful discharge of firearms on school property" with "school shooting" is therefore, in my eyes, hopelessly naive at best and intentionally deceptive at worst.  That changes the context.