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RSS FeedJanuary 28th, 2012
Teaching Unix System Administration at GWU
During the spring 2012, I am teaching Unix system administration at GWU, which is a mix undergraduate and graduate class. Most of the students are graduate students, and they bring a lot of interesting perspectives to this class. When we finish this class in May, there is a small likelihood that the following scenario plays out somewhere:
January 15th, 2012
Defining the center – Mean, Average, Geometric Mean, Median, Mid Range, or something else?
Frequently, the need arises to define the central value of a given population. While the problem is a bit harder in sociology (for example, what does an average American want?), the problem is easier when considering the scientific world, where the population is given by a sequence of numbers.
Here are some of the many concepts that are used to define the central value. A central value tries to represent the population, and is almost never perfect. It may be tricky to decide which of these concepts to use to define the central value.
- Arithmetic mean (also sometimes simply called mean or average) is the average, that is SUM of all numbers, divided by n. For example, the arithmetic mean of 1, 2, 3, 4, 5 is 3.
- Median is the middle entry in the sorted sequence. For example, the median of 1, 3, 4, 10, 17 is 4. If there is an even number of values, then just take the average of those two. For example, the median of 1, 3, 8, 10, 21, 25 is the average of 8 and 10, that is, 9.
- Geometric mean is the 1/n th root of PRODUCT of all numbers. For example, the geometric mean of 1, 2, 3, 4, 5 = 5th root of (1 * 2 * 3 * 4 * 5), that is 5th root of (120). That comes to be about 2.6.
- Mode is the number that appears most often. For example, given 1, 1, 2, 2, 2, 3, 3, the mode is 2.
- Range is simply the range, that is the minimum and and the maximum, and therefore it is not really one central value. For example, the range of 1, 4, 1000 is [1, 1000].
- Mid-range is the middle value of the range. For example, for 1, 4, 1000, the mid-range is 500.5
Here are some observations on these central values:
- When you have numbers that are in a arithmetic series, like 1, 2, 3, 4, 5 (step size is 1) or 2, 5, 8, 11, 14 (here step size is 3), then the average is approximately the middle number. For example, for population [1,2,3,...99,100], the average is 50.5.
- Similarly, for all numbers from 300 to 500, the average is 400. (Obviously).
When to use Arithmetic Mean versus Geometric Mean
- The arithmetic mean is a good measure when numbers are of the same order of magnitude – like students scores on a test.
- Geometric mean would be appropriate if the numbers are in different ranges (ballparks) entirely and you do not want one very large number to affect things that much.
- For example, if you have following numbers: 1, 10, 100, 1000, 10000, the average is more than 2200. But a more appropriate “middle” number is 100 in this case. And 100 is the geometric mean here.
- Real world example: 0.98, 8.7, 121, 1400, 9000. From these 5 numbers, arithmetic mean is about 2100. That number hardly means anything. Geometric mean is about 105, which represents more of a central point.
- Interestingly, median is also a good measure in the previous case. But one problem with median is that the largest number (9000) was changed to 10,000 or 10 million, then still the median would be 121, and would not change at all. However, the geometric mean would change (increase) a bit. Arithmetic mean would change TOO much.
- Yet another scenario where geometric mean is more appropriate than arithmetic mean is when the numbers are given as percentage increases or decreases, rather than absolute values. For example, if the housing market rose 40% 1 year, dropped 40% next year, then an appropriate representation of average growth rate can be found by taking a geometric mean of 1.4 and 0.6, which comes up to be about 0.91, that is about 9% drop. The arithmetic mean would have conveyed a 0% average change.
November 4th, 2011
Grading on a curve, “Yahan ka system, hi hai kharab” and Sir Ken Robinson
A generation ago, I was a student at IIT Delhi. But, I wasn’t a brilliant student. Had a fundamental disconnect with the grading process there – 12.5% of students (roughly, rounding etc) had to be given A, A-, B, B-, C, C-, D and F grades. (All grades other than F are considered passing grades). While there were some professors who deviated from that significantly (and certainly didn’t hand out F grades), that still was the suggested grading policy. That bothered me significantly. Should I hope for my friends to mess up royally, so that I can get a better grade? Should I help someone else study, and in the process, screw my own grade? Should I lend you the book so you can push me to a different color of the pie chart? Even more innocuously, should I really study hard, and in the process push you down one bit? (Really, what kind of friend am I?)
Call it the Buridan’s ass, the obstinacy of the teenage years, or give it a fancier name, but when the system bothers you, you write and sing songs like purani jeans aur guitar and repeat “yahan ka system, hi hai kharab”. 
And now, how the times have changed. Some of my students at GWU ask me, “Would you be grading on a curve?” There is optimism in their voice. The answer they are looking for is “YES!”. “Most definitely!!” “¡Cómo no!” I kind of understand that. The students who are hoping that I grade on a curve, are suggesting that their score may be lower than my “flat passing line”, so if I grade on a curve, they stand to benefit. But alas, I deny them that very easy pleasure. I remind my students that I am going to grade everyone individually, and that I am not bound to give 20% As, 40% Bs and 20% Cs etc. All of them may finish with an A. Or, all of them may finish with a B. One student’s grade is independent of how well the entire class does. The simple reason I do this is to promote goodwill among the students, and to encourage collaboration (wherever appropriate).
In the collaborative aspect, I am in extremely distinguished company. In this awesome video, Sir Ken Robinson, international adviser on education in the arts talks about how the current education system stifles creativity, rather than encouraging it.
October 10th, 2011
Locating a Distribution Center
Locating a Distribution Center is perhaps the most commercial application of the general facility location problem in computer science. Consider a retailer which imports goods for selling in three cities, Indianapolis IN, Columbus OH, and Lexington KY. Further, suppose that this retailer uses an ocean carrier, and the port of call is Norfolk. In that case, where should the distribution center be located? Here is a map view:
August 11th, 2011
School of Life (or, Life in School at 18)
Had an excellent meeting yesterday with a tech superstar (let us call him Dave). Dave has worked in (and sold) many companies, designed a real time operating system, developed a programming language currently in use, designed uber cool software components still being used by a big name ERP software provider. When I asked him about his educational background, Dave casually mentioned that he didn’t have much. Really, no big surprise there – some very big names in software have come from all kinds of schools, and some very big names have been dropouts etc, and some never stepped inside school to begin with. The value of school of life is well understood.
Also well understood is that there are many aspects of formal education which helps many people have a better grasp of their work. Some concepts are easier learnt in a structured program (at least for many people), than in a work environment.
In a certain respect, direct high school -> college -> graduate school -> job route can be considered to be a bottom up approach. Students have a structured path of learning, and they learn all the base steps and continue to build on those blocks, and are then ready for a super job. (Does this approach look similar to Dynamic Programming to you?) Along the path, students may question the relevance of certain classes, and can get a bit frustrated if neither the professor’s lucid explanations and war stories, nor the associate dean’s topological sort dependency diagram of classes are readily available.
The alternate route, high school -> job -> undergraduate -> job -> graduate route can be considered to be a top down, or greedy approach. Students start by learning what they can at their job, figure out what more they need to learn, go back to school to get their undergrad. Some go for masters after they have been working for a while, and benefit from what they learn. They have learnt the processes at work, are aware (somewhat) of the gaps that they have in their knowledge, and are now interested in filling those gaps.
[Umm, and there is also the slight issue of expectations. A person with the title of a senior developer with a graduate degree under his belt walks into his new job and everyone is aghast to find out that he doesn't even know how to use subversion - "Holy BSD!!" There aren't many graduate schools in the world that are going to teach someone how to use version control, and that is also not something that hard to learn, but you do have to learn it. A kid out of high school walks in, and everyone is happy to help him check it out.]
The alternate route is the part where I have picked some of my own arguments with the rest of the academic community. Everyone learns differently, and thus either of these routes may be the right path for someone. The kids shouldn’t just go to college by default when they finish the high school. In my opinion, the freshmen are generally thinking along these lines:
I could be flipping burgers at the King
Touring the Amazon, the pyramids and the sphinx
Working a bit, saving a bit
Climbing the mountains and walking along the Ganges.Instead, I am in this classroom
The professor knows nothing, the college feels like a hoax
The PhD Dude can’t even remember my name
But at least I am four hours away from my folks.
Currently, “living by yourself” has become a very significant portion of the college life, so much so, that everyone says - “Of course, that is a part of the college experience.” That may be the case, but if we can change a situation a bit, the kids can learn to live on their own, as well as, use the college for the kind of education experience that it was meant to provide. Kids can work a bit after high school, travel a bit, study a bit. Maybe go for an Associates degree. Then, when they are 21 or so, maybe then they feel like extending that Associates into a complete Baccalaureate, perhaps graduating when they are 23/24. That is 2 years behind the norm now, but by that time, they would have gotten some work experience, have smaller student loans and have wider perspectives on life and the world – what’s not to like about that?
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Do you have an opinion on this matter?
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