A Mathematics Riddle

Not even sure if I should expose my ignorance (or that of others) here. But this question has been bugging me for a few years now. And I don't see any street protests by mathematicians anywhere. So may be I am wrong. But let me get the bug out of my system anyway.

A percentile is a great invention, by someone who wanted to compare people. As scales go, it is supposed to measure things on an ordinal, or comparative, scale. By definition, it is the number of people below you, if your percentile score is being discussed. If I have a 75 percentile, it should mean that 75% of the students who took the exam with me are below my score (whatever the raw score- that could be 5, or 50, or even 0, if negative marking is allowed, coz some would score minus marks in such a scenario).

Now, a percentile score of 100 is an impossibility by this definition. Because you are one of the people who make up the 100% of the test-taking population. Therefore, you necessarily have to exclude yourself while stating your percentile score- if 100% of the people were below your score, then who are you (only in a limited, not an existential, sense) ?

I have a major problem here. Hope the CATs of tis world and the reporters (don't know if they have a stats course) will solve this riddle for me.

Meoww!

Guide to Management Core Subjects-Statistics

It's one of the most misunderstood subjects in the world. Usually because (pardon me teachers) it is taught badly. With no appreciation that it can do wonders for you, if you don't seek perfection from it (like with most things in life, I might add).

Statistics is the art or science of estimating things, and sometimes calling these predictions- they are still estimates, and can be wrong to varying degrees. But within its limitations, you can estimate a lot of things using simple statistics. For instance, people visiting a store on a given day, or time of the day, can be observed, mapped, and used to determine how many staff would be needed, for example, at what times.

Or, you can look at purchase patterns and send out promotional offers to customers most likely to buy. Online marketers seem to have cottoned on to this, coz I am flooded with pop up ads for air tickets, if I have just browsed for a particular sector on yatra, without buying the ticket.

The trouble is, teaching starts at the wrong end- the theory, which is worse than nuclear physics, and hardly anyone understands it. Practice or application might be the place to start, and present a practical problem, and then go back to how statistics could help solve it (with a margin of error, naturally). And the discussion of errors of all kinds (Type 1, Type 2 are the least of them) goes on and on, that by the time you are done listing all of them you forget what problem it was you were trying to solve.

The other extreme is trying to fit a problem to a technique. As in, I want to use Regression (or Multidimensional Scaling, or whatever). How do I use it in my research? Or, after a questionnaire for a survey has been filled up, saying I want to use x,y,z, technique for analysis. That is like trying to fit a square peg in a round hole, surely? The scale of measurement determines what analysis can be performed. QED.

I will not even talk about probability, until I have understood how to make it better understood.