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Populations, Samples and Estimation.
Consider 3 quite different scenarios.
1) A manufacturer of electronic fuses needs to know the maximum amps at which
a any one of a batch of fuses will burn out. Testing every one to destruction will
leave none to sell, so a few of them are examined to get an idea of the properties of
the batch as a whole.
2) The government of a large country needs to know what proportion of the
population will be eligible for benefits in a health program directed at preventing a
particular disease. It is not possible to examine everyone in the country for
susceptibility to the disease (some of whom will have died and others who will
have born during the examination process) so a much smaller group of individuals
is examined in order to gage the likely proportion in the population that are
susceptible.
3) A local authority, responsible for providing an emergency response team for car
crash victims on a collection of highways, needs to know the likely monthly
frequency and location of crashes in order to establish the size of, and resources
for, the response team. The location and number of crashes per month in recent
history is used as a guess of what the likely locations and frequencies would be.
Each of these three cases has all the characteristics of the problem facing a
statistician, the need to glean some information about an always obscure and often
large collection of things  the Population of Interest  by examining a much
smaller and very real sub group of that collection  The Sample.
When every element in the population is identified and the relevant characteristic
recorded, the resultant data set is referred to as A Census; it constitutes a complete
record of The Population of Interest. It is not necessarily an infinite list (the
complete batch of fuses could certainly all be examined, the population of a
country could certainly all be counted at a point in time) though sometimes it is
(the number of places that accidents could take place in a highway system is
infinite and the theoretical frequency with which they occur on average over a
given period of time is certainly obscure and unobservable). When for various
reasons (economic, feasibility, or practical) a census cannot be taken, the
Population of Interest is something about which we can only conjecture. Typically
in statistics the characteristic of the population we are interested in is treated as a
random variable and a probability density function (p.d.f.) is used to describe its
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View Full Documentdistribution across the range of potential values. One of the arts of practising
applied statistics is that of choosing the right distribution for the problem at hand
and estimating the parameters upon which the distribution depends.
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 Spring '11
 Kambourov

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