Average

=:The Average Presentation:=
-------------------------------------------

What is an average?

•An average refers to a measure of the “middle” of the data set.
•Average is also known as central tendency.
•The most common method of finding the average is using the arithmetic mean.
–Arithmetic mean is the some of all measurements divided by the number of observation in a data set.
Average = (Sum of all the terms) / Number of terms
---------------------------------------------

Oscar Chisini

•He was algebraic geometry researcher.
•Obtained a degree in mathematics in 1912.
•He was involved in original reconstruction of mathematical theories.
•Introduced ‘Chisini mean’ in 1929
–Chisini mean includes arithmetic mean, geometric mean, harmonic mean, etcetera.
•He taught mathematics at secondary school level. And that led him to reflect on the notion of mean, eventually giving an original definition .
-------------------------------------------------

What is average used for?

•The average is used to calculate what is the most common reading in a set of reading.

•In science,
–The average is calculated to minimize the margin of error in an experiment
•The higher the number of replicates, the more accurate the results
–Then it is used to plot a graph
~The graph is then used in report and conclusions.

•In other areas,
–Observations are compared against the average which is used as a standard.
~Conclusions can be then be drawn from the comparison.
---------------------------------------------------------

What was average initially used for?

•The original meaning of the word is “damage sustained at sea”

•This damage or general average, is borne by the owner of the damaged property
–The owner can claim a proportional contribution from all parties to the marine venture

•The type of calculation used in adjusting general average gives rise to today’s arithmetic mean.
------------------------------------------------------------

Evaluating average…

•The problems with arithmetic mean:
–Greatly influenced by outliers.

•Outliers are singular observation far from the rest of the data.

•Consider a set of data, (1, 2, 2, 2, 3, 9).
–The arithmetic mean is 3.17 but five out of six of the numbers are lower than that!

•In these cases, other measures of central tendency should be considered.
----------------------------------------------------------------

Can statistics be subjective?

•Consider a group of 12 people with varying amount of money.
In ascending order: 5,10,15,17,20,22,26,27,30,30,35,107

•Arithmetic Mean =(5+10+15+17+20+22+26+27+30+30+35+107) / 12
=$27.33

•Median=(26+27)/2
=$26.50

•Mode = $30.00

•Interquartile mean = (17+20+22+ 26+27+30)/6
= $20.67

•Midrange Mean = (5+107)/2
= $56.00

•Depending on the what the statistics is used for, the average used will also vary.
–If one going to give away the amount of money that is equal to the average, than lowest average found will be considered.
–If one is receiving money according to the average amount, than the highest average willl be taken.

•Each central tendency has its own value and brings across different findings when used.

•Certain values are omitted in calculation, for example interquartile mean.
–This can be seen as doctoring results or making the result more accurate.
•Therefore, can statistics truly be objective?
-------------------------------------------

Biblography.

•Teknomo, Kardi. Mean or Average. http:\\people.revoledu.com\kardi\ tutorial\BasicMath\Average•Weisstein, Eric W. "Mean." From Mathworld--A Wolfram Web Resource. http://mathworld.wolfram.com/mean.html
•Luca La Rocca. Oscar Chisini. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Chisini.html
Read also: How to lie with statistics, Darrell Huff

3. ‘There is nothing more objective than the laws of mathematics.’ Discuss. Making reference to the mathematical and at least one other mode of inquiry to illustrate your argument.


I would disagree that mathematical inquiry is objective but I would agree that it is more objective than other modes of inquiry.

Firstly, how does a “mode of inquiry” qualify as objective? Does it have to be void of emotions or biased opinions? I believe is such a guideline is applied then mathematics does not qualify as purely objective.

Take statistics for example. Statisticians use mathematics to calculate averages. Arithmetic mean, midrange mean, interquartile mean are some form of averages. All of them have different formulas and all of them lead to different results but all can be used to calculate the average. Depending on what kind of argument the statistician wants to bring across, a different average is used. Biasness over certain results is displayed and the desired result can be obtained. How can we say that statistics or mathematics is objective in this case?

But mathematics can be objective when it is used in calculations such as Newtonian Mechanics found by Sir Isaac Newton to determine something like the velocity of a celestial body, or its position in space.

Mathematics that we apply in everyday life has certain basis to it and it relies on a few axioms. Then there is pure mathematics or abstract mathematics that has nothing to do with everyday life. The law of pure mathematics holds through only in that persons mind until it can be applied in real life. It would be more accurate to call these laws subjective.

Ancient mathematicians found a “Golden Ratio”, denoted by phi. It is approximately 1.618. This ratio can be found in spiral objects ranging from sea shells, sunflowers and galaxies. Johannes Kepler once described phi as one of the “two great treasures of geometry” In nature, this ratio is nothing more than approximations, but it shows that there is something common in objects around us. This is one of the more objective results of mathematics.

Though it is not fully objective, I find it more objective than other modes of inquiry.

Let us consider scientific inquiry. One is required to construct hypothesis and observe an experiment to prove the hypothesis. If the results do not tally with the hypothesis, the hypothesis is revised to obtain a more accurate one. If the revised hypothesis does not suit the results, then it is discarded and a new one is form. Scientific inquiry is based on empiricism where experience plays a heavy role in it.

When something is based on experience, the conclusion is often open to interpretation. The same incident can mean radically different things to two different people. This is because these two have different upbringings, different opinions about things or may be just plain bias, therefore there can be alternate explanation for the same incident. But in mathematics, when the same set of number is used in the same equation by two different people, no matter how much they differ in thinking, biasness or upbringing, as long as their results are accurate, than the result will be the same.
Do not forget the whenever we use an instrument to measure something, we will somehow alter the observe results. One must remember Heisenburg’s Uncertainty Principle that state that we cannot determine something as it truly is. For example if we want to observe an electron, we have to fire some sort of “light” to see it. But this will excite the electron and promote it to a higher than expected energy level.

I do believe that mathematics will not be implicated by the Uncertainty Principle as nothing is disturbed in the calculation other than the medium perform the calculations. This holds true unless empirical measurements are made.

Other than science and mathematics, philosophy is also used to acquire knowledge.

Different philosophers have different views of obtaining knowledge. Some uses skepticism, where they believe that nothing is for certain. Others believe in pragmatism, where only the concept or theory that contributes the most good to the society is true. There are other forms such as idealism, rationalism, contextualism and etcetera.

The concept of good and evil is rather subjective. What is good for majority may be bad for the minority. And the concept of good and bad is used heavily in pragmatism. Two pragmatist that has different concept of good and evil will have different conclusions. This shows that pragmatism is subjective.

There is also the matter of upbringing of the philosopher, where he studied and his views on certain things. The same matter can mean different things to different philosophers just like how the same result can mean different things to different scientists. The conclusion that a philosopher draws is therefore relative and holds true only for the people that have the same thinking as the philosopher.

There are many epistemological approaches but some of them have conflicting views while some support one another. Take for example idealism and materialism. One believes in ideal forms while the other in material items. One may have to alter his philosophical findings to suit his school of thought or it may strengthen the opposition or destroy that school of thought entirely.

In conclusion, although mathematics is not absolutely an objective mode of inquiry, rather, it is the most objective as compare to philosophical inquiry and scientific inquiry. At this point in time, I do believe that nothing is absolute in being objective