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Friday, 18 December 2015
Diagrammatic representation of data - Statistics
Diagrammatic representation of data.
Bar Diagram
Simple Bar diagram.
Multiple Bar diagram.
Component Bar diagram.(Subdivided)
Percentage Bar diagram.
Pie chart
Pictogram
Statistical maps or cartograms.
Bar Diagram
Simple Bar diagram.
Multiple Bar diagram.
Component Bar diagram.(Subdivided)
Percentage Bar diagram.
Pie chart
Pictogram
Statistical maps or cartograms.
Thursday, 17 December 2015
Today In History. What Happened This Day In History
December 16
| 1431 | Henry VI of England is crowned King of France. | |
| 1653 | Oliver Cromwell takes on dictatorial powers with the title of "Lord Protector." | |
| 1773 | To protest the tax on tea from England, a group of young Americans, disguised as Indians, throw chests of tea from British ships in Boston Harbor. | |
| 1835 | A fire in New York City destroys property estimated to be worth $20,000,000. It lasts two days, ravages 17 blocks, and destroys 674 buildings including the Stock Exchange, Merchants’ Exchange, Post Office, and the South Dutch Church. | |
| 1863 | Confederate General Joseph Johnston takes command of the Army of Tennessee. | |
| 1864 | Union forces under General George H. Thomas win the battle at Nashville, smashing an entire Confederate army. | |
| 1930 | In Spain, a general strike is called in support of the revolution. | |
| 1939 | The National Women’s Party urges immediate congressional action on equal rights. | |
| 1940 | British troops carry out an air raid on Italian Somalia. | |
| 1944 | Germany mounts a major offensive in the Ardennes Forest in Belgium. As the center of the Allied line falls back, it creates a bulge, leading to the name–the Battle of the Bulge. | |
| 1949 | Chinese Communist leader Mao Tse-tung is received at the Kremlin in Moscow. | |
| 1950 | President Harry Truman declares a state of National Emergency as Chinese communists invade deeper into South Korea. | |
| 1976 | President Jimmy Carter appoints Andrew Young as Ambassador to the United Nations. | |
| 1978 | Cleveland becomes the first U.S. city to default since the depression. | |
| 1998 | The United States launches a missile attack on Iraq for failing to comply with United Nations weapons inspectors. | |
| 2003 | President George W. Bush signs the CAN-SPAM Act of 2003, which establishes the United States’ first national standards regarding email and gives the Federal Trade Commission authority to enforce the act. | |
| Born on December 16 | ||
| 1485 | Catherine of Aragon, first wife of Henry VIII, who bore him six children; only one, Mary I, survived to adulthood. | |
| 1770 | Ludwig Van Beethoven, German composer best known for his 9th Symphony. | |
| 1775 | Jane Austen, novelist (Sense and Sensibility, Pride and Prejudice). | |
| 1917 | Arthur C. Clarke, English science fiction writer (2001: A Space Odyssey) | |
| 1932 | Sir Quentin Saxby Blake, illustrator and children’s writer; received the Hans Christian Andersen Award (2002) and was Britain’s first Children’s Laureate (1999–2001). | |
| 1936 | Morris Dees, activist; co-founder of the Southern Poverty Law Center. | |
| 1938 | Liv Ullmann, Norwegian actress and director; won Golden Globe for Best Actress–Motion Picture Drama for The Emigrants (1971). | |
| 1943 | Steven Bochco, TV producer and writer (Hill Street Blues, L.A. Law). | |
| 1949 | Billy Gibbons, sinner, songwriter, musician with ZZ Top and Moving Sidewalks bands. | |
| 1955 | Prince Lorenz of Belgium, Archduke of Austria-Este. | |
| 1962 | William Perry, pro football defensive lineman nicknamed The Refrigerator because of his size. | |
| 1963 | Benjamin Bratt, actor best known for his role of Rey Curtis on the Law & Order TV series. | |
| 1969 | Adam Riess, astrophysicist; shared 2006 Shaw Prize in Astronomy and 2011 Nobel Prize in Physics for providing evidence the expansion of the universe is accelerating. | |
Monday, 14 December 2015
Introduction of Correlation Coefficient (CORRELATION)
Correlation
Univariate analysis: Analysis of data when only one variable is involved.
Eg. Dispersion, Central tendency, Skewness, Kurtosis
Bivariate analysis: It is the analyses of data which involves two variables
which have got realtionship exist between them. In biological experiment the
bivariate analysis is very common where in one may like to know the strength of
relationship or one may like to predict one variable from another related
variable.
These techniques help in measuring the independence or
relationship between bivariate data and predict the data of one variable for
the given value of the other variable.
Correlation Coefficient
Correlation analysis is helpfull in ascertaining the strength of
relationship between the two variables. It measures the closeness of relationship
between the two variables.
It ranges from -1 to +1 and it does not have any unit.
It ranges from -1 to +1 and it does not have any unit.
Francis Galton was the first person who investigated the
correlation technique graphically. However Karl Pearson (1857-93) introduced
a method of assessing correlation by means of the coefficient of correlation.
Eg: Milk production and the fat percentage feed intake and
weight gain.
The statistical tool with the help of which the realtionship
between the two variables studied is called correlation.
Correlation and causation
High degree of correlation exists due to any one or a
combination of the following reasons.
1. By
Chance: Due to small number of variables sometimes there may exist a
correlation in a sample but the same does not exist in the population. It is due
to chance factor in small sample.
2. 2.
Influence of some external factors on two variables. A high degree of variables
may be due to same causes affecting the each variable.
3. Influence
of two variables on each other or mutual influence.
4. Influence
of one variable upon the other -one of the variable is truly independent and
therefore acts free from any external forces and influence the other variable
which is truly dependent since it reacts in response to the independent
variable.
Types of correlation:
1. Positive
or negative correlation.
2. Simple
partial or multiple correlations
3. Linear
or non linear correlations.
Positive or negative correlation.
It depends on the direction in which the variables are moving.
When both the variables move in the same direction it is positive correlation
and if they move in the opposite direction it is negative correlation.
Simple , Partial & Multiple correlation
Simple- Only two variables are involved.
Partial or multiple- Relationship of more than two variables.
Multiple correlation- The relationship between one independent
variable and two or more independent variables are studied.
Eg. Feed intake _ Body weight, Milk yield.
Partial correlation: The study of two variables excluding some other variables is
called partial correlation.
Linear and non Linear correlations:
Correlation between two variables is said to be linear if
corresponding to a unit change in one variable, there is a constant change in
one variable, there is a constant change in the other variable over the entire
range of values.
X
30
60
90 120
150
Y
10
20
30
40 50
The graph of these variables having such relationship will form
a straight line.
The distinction between linear and non- linear correlation is
based on the ratio of change between the variables under study.
X
1
2
3
4 5
Y
5
7
9
11 13
Thus for a unit change in X there is a constant change of 2 in
Y.
Y = 2X + 3
The two variables X and Y are linearly related, if there exist a
relationship
Y = a + bx
That is if the two values are plotted on a graph one should get
a straight line.
If there is no constant change in ‘Y’ for every unit change in
‘a’ then it is termed as non linear or curvilinear.
Non linear – eg.
If we double the protein content in the feed milk, production will not be
doubled. The graph of non- linear realtionship will form a curve. It is also called
“curivilinear
relationship”.
The mutual relationship could depend on
1. Mutual
dependence- supply and demand
2. Both are
influenced by same external factors – Effect of weather on rice and potato
yield.
3. Pure
chance- size of shoe and degree of intelligence- known as spurious or non sense
correlation.
Methods of studying correlation
I. Scatter
diagram method: By plotting the two variables on the graph sheet the
relationship can be understood. If the points are too much scattered it
indicates less or no relationship. If it is condensed then it indicates some
relationship between the two variables.
Depending upon the
distribution in the scatter plot
1. High degree of
positive correlation
2. High degree of negative
correlation
3. Low degree of negative
correlation
4. Low degree of positive
correlation
This method does not
get affected by extreme values and give fair degree of relationship. However,
in large sample it is not suitable. It does not provide exact measure of the
Merits and Demerits of scatter diagram
Merits:
1.Simple
2. We can have a rough idea about the realtionship whteher it is
+ve or –ve.
3. Not influenced by extreme item.
Demerits
It cannot give exact degree of correlation
II. Graphical
method The two individual values of the two variables are plotted on a graph
paper. We thus get two curves one for X and another for Y. These two curves
form the basis of comparison.
Jan Feb Mar
Apr May
VariableI
12
16
12
14 18
Variable II
18
14
18
16 13
Both these are about visualizing relationship.
III. Coefficient
of correlation _ Measuring the relationship.
Karl Pearson developed the method
It is also called Pearsonian Coefficient of correlation
Applications of Operations Research - Notes
Scope of Operations Research
Any problem,
simple or complicated, can use OR techniques to find the best possible
solution. This section will explain the scope of OR by seeing its application
in various fields of everyday life.
In Defense Operations:
In modern warfare, the defense operations are carried out
by three major independent components namely Air Force, Army and Navy. The
activities in each of these components can be further divided in four
sub-components namely: administration, intelligence, operations and training
and supply. The applications of modern warfare techniques in each of the
components of military organisations requireexpertise knowledge in respective
fields.
Furthermore, each
component works to drive maximum gains from its operations and there is always
a possibility that the strategy beneficial to one component may be
unfeasible for another component. Thus in defense operations, there is a
requirement to co-ordinate the activities of various components, which gives
maximum benefit to the organization as a whole, having maximum use of the individual
components. A team of scientists from various disciplines come together to
study the strategies of different components. After appropriate analysis
of the various courses of actions, the team selects the best course of action,
known as the µoptimum strategy.
In Industry:
The system of modern industries is so complex that the optimum
point of operation in its various components cannot be intuitively judged by an
individual. The business environment is always changing and any decision useful
at one time may not be so good some time later. There is always a
need to check the validity of decisions continuously against the
situations. The industrial revolution with increased division of labor and introduction
of management responsibilities has made each component an independent unit
having their own goals. For example: production department minimizes the cost
of production but maximizes output. Marketing department maximizes the output,
but minimizes cost of unit sales. Finance department tries to optimize the
capital investment and personnel department appoints good people at minimum
cost. Thus each department plans its own objectives and all these objectives of
various department or components come to conflict with one another and may not
agree to the overall objectives of the organization. The application of OR
techniques helps in overcoming this difficulty by integrating the diversified
activities of various components to serve the interest of the organization as a
whole efficiently. OR methods in industry can be applied in the fields of
production, inventory controls and marketing, purchasing, transportation and
competitive strategies.
Planning:
In modern times, it has become necessary for every government to
have careful planning, for economic development of the country. OR techniques
can be fruitfully applied to maximize the per capita income, with minimum
sacrifice and time. A government can thus use OR for framing future economic
and social policies.
Agriculture:
With increase in population, there is a need to increase
agriculture output. But this cannot be done arbitrarily. There are several
restrictions. Hence the need to determine a course of action serving the best under
the given restrictions. You can solve this problem by applying OR techniques.
In Hospitals:
OR methods can solve waiting problems in out-patient department of
big hospitals and administrative problems of the hospital organisations.vi)
In Transport:
You can apply different OR methods to regulate the arrival of
trains and processing times minimize the passengers waiting time and reduce congestion,
formulate suitable transportation policy, thereby reducing the costs and time
of trans-shipment.
Research and Development:
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