|
Errors:
|
|
1. A continuous variable can never be
measured with perfect finances because of certain habit and practices, method
of measurements etc.
2. Measurements are usually recorded to the
nearest units i.e. inch, pound, k.g etc.
3. They are therefore seldom exact, mostly
they are approximate, “the difference between the measured value and the true
value” however small it may be is called the error of measurements. e.g. if a
student’s weight is recorded as 60 kg (correct the nearest k.g) is true
weight infect lies between 59.5 kg and 60.5 kg. These there is the difference
between the measured value and the true value.
|
Saturday, 29 October 2016
Errors:
Wednesday, 26 October 2016
Kinds of Constant
|
Kinds
of Constant
|
|
|
1.
Arbitrary
constants غیر مطلق مقدار
|
2.
Absolute
constants مطلق مقدار
|
|
Definition:
A constant is called
arbitrary constant if it has fixed value in a particular values in different
problems.
Denoted:
a, b, c…….
|
Definition:
These are the quantities
which have the same value in all problems.
Examples:
1,2,3,4 are known as absolute constant.
|
|
ایسی
مقداریں جو ایک ہی سوال کے سوال اپنی قیمت نہیں بدلتیں البتہ مختلف سوالات کے
دوران مختلف قیمتیں اختیار کر سکتی ہیں۔
|
ایسی مقداریں جو کسی حالت میں
بھی اپنی قیمت نہ بدلیں مثلاً 15 ، -4/5، -1/2
|
|
Note:
|
|
|
1.
Variable X,Y,…. Are also called “Unknown
quantities”
2.
Constant a,b,c…. are also called “known
quantities”
|
|
Constant:
|
Constant:
|
|
|
Definition1:
A measureable
quantity which can assume one and only one value is known as constant.
|
Definition2:
A quantity which does
not change in a problem is called constant.
|
|
Examples:
1.
Value
of g = 9.8m / sec2
2.
Value
of
3.
Value
of e = 2.7183
A
constant is usually denoted by first letters of alphabets A,B,C,D etc.
|
|
Variable: Kinds of Variables:
|
Variable:
|
|
Definition:
“A characteristic which changes from one individual to another
is called a variable”.
|
|
Kinds of Variables:
|
|
|
1.
Discrete variable
2.
Continuous variable
|
3.
Quantitative variable
4.
Quantitative variable
|
|
1.
Discrete variable
|
2.
Continuous variable
|
|
Definition1:
A variable that can assumed only
specified values between a set of a values that is the values are taken by
jumps, is called discrete variables.
Definition2:
A discrete variable takes on values
which are integers or whole numbers”
Examples:
1.
Number of pages in a book.
2.
Number of rooms in a house.
3.
Price
4.
Income
5.
Saving
6.
Consumption
7.
Number of children in family can
be 0,1,2… but cannot be 2.5 or 3.84
|
Definition:
“A
variable that can assume any value either fractional or integral between two
specified limits is called continuous variables”.
Examples:
1.
Heights and weights are students.
2.
Speed of a car or jumps.
3.
Temperature.
4.
Rain fall.
5.
Weight of a person.
6.
Height of a plant.
|
|
Quantitative
variable
|
Qualitative variable
|
|
Definition:
“A characteristics whose change is
expressed numerically is called quantitative variable”
Examples:
Heights, weights, age , income etc.
|
Definition:
“A
non-numerical characteristic which vary in quality is called qualitative
variable or attribute”.
The
data determined from a qualitative variable are called qualitative data.
Examples:
Education,
poverty, sex, beauty
|
Observation:
|
Observation:
Definition;
“In statistics, numerical measure of
some condition is called an observation.”
The
work of statistics may be called statistical work. The statistical work
starts with a set of observations. The
observations may be the wages of workers in factories, the number of
accidents per day on the roads and so on.
Thus
we start with observations.
Observations are the take off point for
statistical work.
|
Statistics
|
Statistics
|
|
Definition:
Any numerical quantity calculated from the sample observation
is called statistic.
An ordinary (x, y, z, a, b, c) letters is used to represent a
statistic.
Examples:
The value of statistic is not
fixed. It varies from sample to sample.
Thus Statistic is a random
variable (chance variable) end is used to estimate the value of population
parameter.
|
Difference b/w Sample and Parameter
|
Sample:
|
Parameter:
|
|
Definition:
The
part of the population is called sample.
Examples:
1.
A food inspector takes a sample
of the food items like milk, flour etc.
2.
To determine where they are pure
or not. Only a few drops of blood from a person are sufficient to reveal the
nature of his health.
|
Definition:
“Any
numerical quantity computed from the population observation is called
parameter.
Example:
Mean
standard deviation. etc.
A
parameter is usually denoted by Greek letters e.g.
It
is important to note that the value of parameter is fixed.
|
Population, Kinds of Population
|
Population
|
|
|
Definition:
“The
collections of all possible observation are called population.”
|
Examples:
1.
The students of a class.
2.
Number of stars.
3.
The number of girls in 1st
year.
|
|
Kinds of
Population
|
|
|
Finite Population
|
Infinite population
|
|
Definition:
It is called finite
if its individuals can be counted.
Examples:
1. The population of
income tax payers the population of smokers in a country.
2. Number of books in
college.
|
Definition:
The population is
called infinite when its individuals cannot be counted.
Examples:
1. The number of hair
on the head.
2. The number of sun
rays.
|
Tuesday, 25 October 2016
Importance of Statistics in Diff, Fields
1.
Statistics and
Business.
Statistics plays an important role in
business. It helps the business to plan production according to the tastes to
plan production according to the quality of products is checked by using
statistical methods. It also enables the businessman to judge the efficiency
of new production methods by studying the relationship between costs and the
methods of production.
|
2.
Statistics and Banking
Statistics plays a vital role in the
field of banking providing up to date knowledge statistics, by giving
information about calls for withdrawals helps bankers to know how much idle
money will be left with them which they can lend and earn profit.
|
3.
Statistics and
Insurance.
Statistics plays an important role in
the field of insurance. i.e. the insurance companies fix the rates of premium
on the basis of estimated interest rates for the future and the mortality
experience is the past statistical date are used to find the death rates in
the past and the state methods are used to estimate the rate of interest for
coming times.
|
4.
Statistics and
Mathematics.
All statistical methods have their
foundations in mathematics. No calculation work can be done without using
mathematics. That is why mathematics is widely used in statistics. The branch
of statistics relating to mathematics is known as mathematical statistics.
|
5.
Statistics and
Physics and Chemistry.
Physics have developed their own
stat-methods like ‘Quantum Statistics’ has given new idea to the qualities of
laws of nature.
Statistical concepts are widely used
in some modern chemical theories. In newly developed science of Bio-Physics
and Bio-Chemistry, we are required the measurement to check the variability
of material. Stat- methods are used to analysis the experimental results and
test their significance.
|
6.
Statistics and Astronomy.
Astronomers
made use of statistics in 16th century. They applied it to compile
records regarding the motion of heavenly bodies for the predictions of
eclipses and positions of stars.
|
7.
Statistics and
Meteorology
In meteorology statistical principle
and methods are used in weather forecasting. Meteorologists have to called
and analyze data which are complex in nature and are affected by some un
control able factors. Use of some stat techniques help in saying something
about the future events.
|
8.
Statistics and Biology.
Stat-methods are widely used in
Biology for the measurement of living organisms like human beings animals,
plants etc. important branch of Biology, Genetics seeks to explain the
resemblances and differences among organisms due to their descent
stat-methods.
In medical field stat- methods enable
us to test the effectiveness of different treatments and medicines.
|
9.
Statistics and
Economics.
Stat-data and stat-methods help to
study the economics problems and provide valuable solutions to these
problems. They also help the policy-makers to formulate the economic
policies. It is statistics which provides a systematic study of markets, law
of prices based on supply and demand etc.
In economic research stat-methods are
used for collecting, analysis the data and testing the hypothesis.
|
10.
Statistics and Sociology.
In sociology, statistics is used to
collect data on various aspects of society and stat-methods are used in
analyzing data interpreting the results. e.g. in population censuses data on
economics and social status of the people are collected social surveys are
conducted to find the state of unemployment housing facilities, causes of
crimes, children problems etc. statistical methods are used at every stage.
|
11.
Statistics and
Psychology.
Statistics plays an important role in
Psychology and education.
In experimental Psychology a problem
is situated by using a sample. A good sample is selected with the help of
statistics. Stat-methods are used to analyze the experimental data and to
draw valid conclusion from it.
In applied Psychology, various tests
are conducted to measure the intelligence and the aptitudes for various jobs
and assignments, stat-methods are used of test the reliability of such tests.
|
12.
Statistics and
Policies.
All government policies are based on
statistical information.
Example.
In order to decide how many new
schools and colleges should be opened data about school and college going
population and the number of schools and colleges already working and the
trend in the growth of population and towards education are necessary. Thus
statistics are the back bone of government Policies.
|
13.
Statistics and
Agriculture
Statistical methods help to study the
comparison of various variables seed or fertilizers. Many agricultural
problem solved by applying some suitable statistical technique.
Agricultural statistics are also help
to make proper planning and for meeting future food requirements.
|
14.
Statistics and
Administration.
Statistics plays a useful role in the
field of administration. A modern administrator whether in public or private
sectors mostly depends upon statistical data. Preparation of budget is
impossible without statistical records.
In Pakistan all the ministries and
Govt. departments depends on statistical data in performing sound and
effective planning.
|
15.
Planning.
Statistics is essential for planning.
All planning is based on information which is statistical in nature. Moreover
the objects and target of planning are to be stated in numbers which are
statistical in nature.
|