Average

=:The Average Presentation:=
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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
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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 .
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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.
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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.
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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.
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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?
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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