Foundation of Statistics
Statistics is fundamentally
concerned with the presentation and interpretation of chance outcomes that
occur in a planned or scientific investigation. Many Statistician, Theorist and
Scientist came in different ages; they define the Statistics differently. Some
consider statistics as mathematical body of science that pertains to the
collection, analysis, interpretation or explanation, and presentation of data while others consider it a branch
of mathematics concerned
with collecting and interpreting data. Because of its experimental roots and
its focus on applications, statistics is usually considered a distinct
mathematical science rather than a branch of mathematics. Some tasks a
statistician may involve are less mathematical; for example, ensuring that data
collection is undertaken in a way that produces valid conclusions,
coding data, or reporting results in ways comprehensible to those who must use
them. Statisticians improve data quality by developing specific experiment designs and survey
samples. Statistics itself also provides tools for prediction and
forecasting the use of data and statistical
models. Statistics is applicable to a wide variety of academic disciplines, including natural
and socialsciences, government, and business. Statistical consultants can help
organizations and companies that don't have in-house expertise relevant to
their particular questions. For example, a Statistician wants to record the
number of accidents that manly occur from the interaction of E.walnut str and S.Galbstone ave in Jordan valley park, Springfield. The Statistician hoping to justify the
installation of traffic lights, he might classify responses in an opinion poll
" Yes" or "No". Therefore, the Statistician is usually
dealing his data either numerical data
or Qualitative data.
In daily life, a person work on
different applications and these all have their own progression to have done
them. Therefore, working on statistics, it’s important to recognize the different
types of data. Data are the actual pieces of information that a person
collect through his studies. For example, if a person asks six of his friends
how many pets they own, they might give him the following data: 0, 6, 2, 1, 4,
18. Not all data are numbers; let’s say a teacher also record the gender of each of his
students, getting the following data: male, male, female, male, female. Most
data fall into one of two groups: numerical or Qualitative.
· Numerical data: Statisticians
also call numerical data as quantitative data. These data have meaning as a
measurement, such as a person’s height, weight, IQ, or blood pressure; or
they’re a count, such as the number of stock shares a person owns, how many
teeth a dog has, or how many pages you can read of your favourite book before
you fall asleep. Numerical data is further broken into two types: discrete and
continuous.
o Discrete
data it take on possible values that can be listed
out. For example, the number of heads in 100 coin flips takes on values from 0
through 100 finite case, but the number of flips needed to get 100 heads takes
on values from 100 the fastest scenario on up to infinity. If you never get to
that 100th heads, it's possible values are listed as 100, 101, 102, 103, . . . representing
the countably infinite case.
o Continuous
data represent measurements; their possible values
cannot be counted and can only be described using intervals on the real number
line. For example, the exact amount of gas purchased at the pump for cars with
20-gallon example tanks would be continuous data from 0 gallons to 20 gallons,
represented by the interval [0, 20], inclusive. You might pump 8.40 gallons, or
8.41, or 8.414863 gallons, or any possible number from 0 to 20. In this way,
continuous data can be thought of as being unaccountably infinite.
· Qualitative data: When
things are grouped accordingly some common property and the number of members
of the group are recorded e.g. males/female, vehicle types.
In Statistics there are two
statistical methods to collection, presentation, analysis and interpretation of
data.
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Descriptive Statistics consist of
those methods concerned with collection and describing a set of data so as to
yield meaningful information. For example, construction of tables, charts,
graphs, and other relevant computation in various newspapers and magazine
usually fall in the area categorized as descriptive statistics. In the other
hand, Statistical Inference comprise those methods concerned with the analysis
of a subset of data leading to prediction or inference about the entire set of
data.
