You have a server farm with a mix of different servers that have been installed

Question

You have a server farm with a mix of different servers that have been installed over time. The program mix they each run is the same as shown in table below.  You are trying to determine your worst performing machine so you can replace it. Using the data provided, determine which machine you would replace. Show your work and justify your answer. 20 points

Execution Times
Program System A System B System C System D System E System F
Web Server 20 15 45 30 40 25
Application Server 105 115 95 155 90 100
Database 175 170 160 115 170 175
All values shown in milliseconds

Which measure of central tendency works best for this type of problem?

Explanation / Answer

The reason we use the median is to avoid the influence of the outliers. If there are no outliers or if they are symmetrically scattered about the mean, the mean would still be quite a good representative of the central tendency.

Here is an example that should tell you why we use median at all and not use the mean every time. Suppose you want to figure out how much the average person in a place makes so that you figure out what that person can afford to buy. Suppose also that a very rich person lives there. If you average the incomes, the rich person's income may well push the mean way higher than what everyone else is making in the town. To make it clearer, let us suppose these are the income numbers in multiples of $10,000 among 11 people: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100 - notice the 11th person making a million.

The average of all these numbers is 155/11, which is well over 10. So, in other words, if you relied on the mean to price whatever you are selling, no one else other than the rich guy would be able to afford it. But the median still gives you a good representative of the central tendency: it is not affected by the millionaire.

Did you know that house price statistics are quoted in medians? A few palatial houses that are worth tens of millions will skew the mean so badly that a prospective house buyer will not know what to expect. But the median gives you a much better idea of how much houses are worth in a neighborhood or a city.

But why do we want to use the mean then? The mean is mathematically very convenient for several things, but these may be well beyond 7th grade math.

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