STATISTICS

Statistics is the formal science of making effective use of numerical data relating to
groups of individuals or experiments. It deals with all aspects of this, including not only
the collection, analysis and interpretation of such data, but also the planning of the
collection of data, in terms of the design of surveys and experiments.

A statistician is someone who is particularly versed in the ways of thinking necessary

for the successful application of statistical analysis. Often such people have gained this
experience after starting work in any of a number of fields. There is also a discipline
called mathematical statistics, which is concerned with the theoretical basis of the
subject.

The word statistics can either be singular or plural. When it refers to the discipline,
"statistics" is singular, as in "Statistics is an art." When it refers to quantities (such as
mean and median) calculated from a set of data, statistics is plural, as in "These statistics
are misleading."

Statistics is considered by some to be a mathematical science pertaining to the

collection, analysis, interpretation or explanation, and presentation of data, while others
consider it to be a branch of mathematics concerned with collecting and interpreting
data. Because of its empirical roots and its focus on applications, statistics is usually
considered to be a distinct mathematical science rather than a branch of mathematics.

Statisticians improve the quality of data with the design of experiments and survey
sampling. Statistics also provides tools for prediction and forecasting using data and
statistical models. Statistics is applicable to a wide variety of academic disciplines,
including natural and social sciences, government, and business.

Statistical methods can be used to summarize or describe a collection of data; this is

called descriptive statistics. This is useful in research, when communicating the results
of experiments. In addition, patterns in the data may be modeled in a way that accounts
for randomness and uncertainty in the observations, and are then used to draw
inferences about the process or population being studied; this is called inferential
statistics. Inference is a vital element of scientific advance, since it provides a prediction
(based in data) for where a theory logically leads. To further prove the guiding theory,
these predictions are tested as well, as part of the scientific method. If the inference
holds true, then the descriptive statistics of the new data increase the soundness of that
hypothesis. Descriptive statistics and inferential statistics (a.k.a., predictive statistics)
together comprise applied statistics.

IMPORTANCE OF STATISTICS
(1) Business:
          Statistics play an important role in business. A successful businessman must be
very quick and accurate in decision making. He knows that what his customers wants,
he should therefore, know what to produce and sell and in what quantities. Statistics
helps businessman to plan production according to the taste of the costumers, the
quality of the products can also be checked more efficiently by using statistical
methods. So all the activities of the businessman based on statistical information. He
can make correct decision about the location of business, marketing of the products,
financial resources etc…

(2) In Economics:
          Statistics play an important role in economics. Economics largely depends upon
statistics. National income accounts are multipurpose indicators for the economists and
administrators. Statistical methods are used for preparation of these accounts. In
economics research statistical methods are used for collecting and analysis the data and
testing hypothesis. The relationship between supply and demands is studies by
statistical methods, the imports and exports, the inflation rate, the per capita income are
the problems which require good knowledge of statistics.

(3) In Mathematics:
          Statistical plays a central role in almost all natural and social sciences. The
methods of natural sciences are most reliable but conclusions draw from them are only
probable, because they are based on incomplete evidence. Statistical helps in describing
these measurements more precisely. Statistics is branch of applied mathematics. The
large number of statistical methods like probability averages, dispersions, estimation
etc… is used in mathematics and different techniques of pure mathematics like
integration, differentiation and algebra are used in statistics.   

(4) In Banking:
          Statistics play an important role in banking. The banks make use of statistics for a
number of purposes. The banks work on the principle that all the people who deposit
their money with the banks do not withdraw it at the same time. The bank earns profits
out of these deposits by lending to others on interest. The bankers use statistical
approaches based on probability to estimate the numbers of depositors and their claims
for a certain day. 

(5) In State Management (Administration):

          Statistics is essential for a country. Different policies of the government are based
on statistics. Statistical data are now widely used in taking all administrative decisions.
Suppose if the government wants to revise the pay scales of employees in view of an
increase in the living cost, statistical methods will be used to determine the rise in the
cost of living. Preparation of federal and provincial government budgets mainly
depends upon statistics because it helps in estimating the expected expenditures and
revenue from different sources. So statistics are the eyes of administration of the state.    

(6) In Accounting and Auditing:

          Accounting is impossible without exactness. But for decision making purpose, so
much precision is not essential the decision may be taken on the basis of approximation,
know as statistics. The correction of the values of current asserts is made on the basis of
the purchasing power of money or the current value of it.
            In auditing sampling techniques are commonly used. An auditor determines the
sample size of the book to be audited on the basis of error.    

(7) In Natural and Social Sciences:

          Statistics plays a vital role in almost all the natural and social sciences. Statistical
methods are commonly used for analyzing the experiments results, testing their
significance in Biology, Physics, Chemistry, Mathematics, Meteorology, Research
chambers of commerce, Sociology, Business, Public Administration, Communication
and Information Technology etc…

(8) In Astronomy:
          Astronomy is one of the oldest branch of statistical study, it deals with the
measurement of distance, sizes, masses and densities of heavenly bodies by means of
observations. During these measurements errors are unavoidable so most probable
measurements are founded by using statistical methods.
Example: This distance of moon from the earth is measured. Since old days the
astronomers have been statistical methods like method of least squares for finding the
movements of stars.

STATISTICAL TERMS
1. Correlation: The relationship that
exists between two variables, x and y. A parameter that is determined by
regression analysis. There can be either positive or negative correlations.
2. Distribution: A representation of the
data in a set, usually presented graphically as a histogram or as a scatter plot.
3. Estimate: An estimate of one value
based on other known data values
4. Experiment: The study of collected
data
5. Experimental unit: The unit of data
that is sampled and studied
6. Mean: A measure of central
tendency of the data, also known as an average. There are arithmetic, geometric
and harmonic means.
7. Median: The middle number in an
ordered data set. If there are an even numbers within a set, the middle two
numbers are averaged to arrive at this number.
8. Mode: The number which occurs
most frequently in a set of numbers. A measure of central tendency in a data set.
9. Outliers: Data which do not seem to
be representative of a data set, due to too large or too small of a value.
Sometimes due to measurement errors.
10. Parameter: A constant value used to
signify a characteristic of the population. Examples are measures of central
tendency or variance.
11. Population: The complete group of
objects that data is drawn from
12. Sample: A portion of the population
that is used to estimate characteristics of the entire population
13. Sampling distribution: The variance
between data collected from a sample and the complete population
14. Statistic: A specific piece of data
from a sample or population
15. Statistical inference: The conclusion
made from analysis of collected data
16. Variance: a mathematical measure
of the variability within a data set.
17. Data means groups of information
that represent the qualitative or quantitative attributes of a variable or set of
variables. Data are typically the results of measurements and can be the basis of
graphs, images, or observations of a set of variables.
18. Raw data refers to a collection of
numbers, characters, images or other outputs from devices that collect
information to convert physical quantities into symbols, which are unprocessed.
19. Standard deviation of a statistical
population, a data set, or a probability distribution is the square root of its
variance. Standard deviation is a widely used measure of the variability or
dispersion.
20. Range is the length of the smallest
interval which contains all the data. It is calculated by subtracting the smallest
observation (sample minimum) from the greatest (sample maximum) and
provides an indication of statistical dispersion.