EDIT 12-12-11  I encourage you to read the comments at the end of this post, including one by Neil deGrasse Tyson himself!  Based on some of the constructive comments and criticisms I’ve gotten here and on Facebook, I’m backing off on the average criticism a bit, but I am leaving it in the post for the purpose of integrity and not pretending like I didn’t say something I did say.

Some of my friends and I went to see Neil deGrasee Tyson speak at SIUE last night (12-7-11).  His talk was very somewhat similar (~25% the same) to his keynote address given at TAM 9 from Outer Space last July, and he made a couple of statements (one of which was repeated from TAM9) that I thought were worthy of a little Cordial Deconstruction.

I know it seems disingenuous to preface a criticism of someone by stating how much you like them, but I’m still going to preface this with the statement that I’m a big fan of Neil deGrasee Tyson, and relish every opportunity to hear him speak, but I did have  problems with a couple of the things he said last night.

An Average Mistake

Dr. Tyson went through a series of slides showing statements made by various people that demonstrate a lack of understanding of science and or mathematics, but his criticism of one of the statements was not very well thought out, in my opinion.  I don’t remember the exact quote, but the essence of the statement was “half of all students are below average”, and Dr. Tyson’s criticism was that this statement was so definitively self obvious as to not require stating.  He said that it was kind of the whole point of average, and that half of any sample would always be below average since average represents the middle.  I know Dr. Tyson understands the concepts of median, mean, and mode, but in spite of that, he apparently didn’t think through his criticism of the statement in that slide.  He made the same point at TAM9, and he apparently hasn’t revised it since then.  It’s just not correct to say that half of any set will always be below average.

Before I can go any further, we have to determine what someone means when they say average.  The most common use of that term is in regards to the arithmetic mean, which is when you add up all the values and divide by the number of values.

I’ll use a simple hypothetical situation with math simple enough to be done without a calculator.  Let’s say I administer a ten question exam to ten students.  Nine students score a perfect 10, and one student scores a perfect 0.

The mean score is 9 ((9*10+0)/10).  In this example using mean for average, 1 student (10%) of the sample scored below average, and 9 students (90%) scored above average.

Sometimes, one might be referring to the median value when they use the term average.

From Wikipedia:

 “Median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half”

By definition would seem to fit Dr. Tyson’s statement.

However, I see two problems here.  Firstly, while it may not be technically incorrect to intend median when referring to the average value, the typical understanding of what is meant by average is the arithmetic mean.  In my opinion, in order to avoid confusion, the use of the word average with general audiences should usually be restricted to refer to the arithmetic mean, and one should say median when they mean median.

The other problem is that even median doesn’t always result in half of a given sample being below average.

Also from Wikipedia:

“At most, half the population have values less than the median, and, at most, half have values greater than the median. If both groups contain less than half the population, then some of the population is exactly equal to the median.”

In the above example, when following the rules used to determine the median value, it comes out to be 10.  Using median for average, 10% of the students are still below average, while 90% are average, and nobody is above average.

There are other things that one could intend when using the term average, such as mode, but these uses would be even more uncommon and really need to be specified when intended.

Initial Mistake

Dr. Tyson also made what in my opinion, was an even grosser misstatement regarding the New Horizons probe to Pluto and the Kuiper Belt.  (To clarify, it was unquestionably a factual misstatement; it is my opinion that the severity of this misstatement is larger than that of his comment about averages.)

He stated that New Horizons was the fastest thing we had ever sent anywhere, and it would eventually overtake the Voyager probes as the most distant man made objects from the Earth.  This is factually incorrect, though there is a grain of truth at the heart of this statement.

While it is true that the New Horizons probe achieved the highest launch velocity of any craft so far, left Earth faster than any other mission or probe, and had the highest initial solar escape trajectory, it neither has the record for highest maximum velocity (the Helios probes hold that distinction), nor is it traveling faster than Voyager 1.  While New Horizons had a higher initial velocity than Voyager 1, Voyager’s velocity was boosted by gravitational slingshots with outer planets to a higher final velocity than New Horizon’s, and New Horizons will never overtake Voyager 1 as the most distant man made object form the Earth (or Sun).

Footnote Acknowledgement of Personal Fallibility

Normally, when I Deconstruct something, I like to be able to review it several times, so I can be sure my Deconstruction is valid, and I am not missing something that would invalidate my criticisms, but the talk last night was live, I can’t review a video of it, and I didn’t take any notes. (Notes would only help me remember things I noticed at the time and would not allow me to look for things that I may have missed anyway.)  As a result, this post was written based on my recall and understanding of what Dr. Tyson said last night (and last July), and is therefore subject to various limitations that could leave me in error in regards to my Deconstruction of the two points discussed in this post.  I therefore acknowledge the possibility that I may have misheard, misunderstood, or improperly recalled the points put forth by Dr. Tyson, and I could be off base on one or both of my criticisms, which is one of the reasons why I allow commenting on my posts, and I invite any relevant commentary anyone might have to add.