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Introduction To Statistics

Statistics: In singular sense “Statistics” is defined as the science of collection, presentation, analysis and interpretation of the numerical data.
In plural sense “Statistics” means the aggregates of numerical facts collected for any purposes in any field of study. The word “Statistics” is also the plural of the word statistic.

Population: A population is defined as the collection of all the objects having some common characteristic of interest. e.g. All the students in Punjab, all houses in a city, etc.

Parameter: A quantity calculated from entire population is called parameter. These are fixed values or constants. Parameters are denoted by Greek letters. µ, etc.

Sample: A sample is defined as a small enough representative part of the population selected with the object that it will represent the characteristics of the whole population.
Statistic: . A quantity calculated from sample is called statistic. These are random variables. Statistics are denoted by Latin letters i.e. X, S, P etc.
Ratio & Proportion:
A ratio of A to B is the fraction A/B. Proportion is a special ratio of a part to its total.
Experiment: It is defined as a process, which generates raw data. A single performance of an experiment is called trail. The result obtained from an experiment is called outcome. The outcome may be success or failure.
Constant: It is defined as a quantity that remains fixed from individual to individual. e.g. e = 2.71828… ? = 3.14159… etc.
Importance of Statistics: Statistics can be applied in every field of research.
1. When Statistics is applied in economics, it is called econometrics.
2. When Statistics is applied in Biology, it is called Biometry.
3. Statistics is applied in social sciences to find relation between certain variables.
4. In plant sciences Statistics is used to design the experiment and drawing conclusions.
5. Statistics is applied in medical sciences to check the effectiveness of new drugs.
Variable: A characteristic that varies from individual to individual in a population is called variable. For example height, weight, speed, number of houses etc.
Fixed Variable:
A variable whose values can be determined before hand is called fixed variable.
Random Variable: A variable whose values vary from one individual to another is called random variable.
Quantitative Variable: A variable, which can assume numerical values, is called quantitative variable. e.g. height, weight, speed, number of students etc.
It has two types. 1- Discrete variable 2- Continuous variable
Discrete Variable: A variable that can take countable number of values or the values with jumps or gaps is called discrete variable. e.g. number of students in a class.
Continuous Variable: A variable that can take all possible values in an interval on the number line is called continuous variable. e.g. height, weight, speed, etc.
Qualitative Variable or Categorical Variable: A variable, which can not assume numerical values but only its absence or presence can be categorized, is called qualitative variable. e.g. sex, eye colour, beauty, honesty etc.
Descriptive Statistics: The branch of Statistics that deals with collection, presentation and analysis of data is called descriptive statistics.
Inferential Statistics: The branch of Statistics that deals with drawing inferences about the population on the basis of sample is called inferential statistics.
Order Statistics: The arrangement of data in order of its magnitude is called order statistics. In order statistics the values are denoted by Y(1), Y(2), Y(3), Y(4), … Y(n)
Datum & Data: A single numerical fact is called datum while a collection of many numerical facts is called data. e.g. the weight of a student of 1st year class is datum while the weights of 100 students of 1st year class is data.
Sources of Data:
There are two types of data. 1- Primary data 2- Secondary data
Primary Data: The raw data that has just been collected and has not undergone any kind of statistical treatment is called primary data. E.g. heights of the new first year class students.
Secondary Data: The data which has already been collected, tabulated and has undergone a statistical treatment at least once, is called secondary data. E.g. list of the marks of all students of college.
Sources of Primary Data: The sources of Primary Data are as follows.
1- Personal investigation 2- Through investigators 3- Through questionnaire
4- Through local source 5- Through internet 6- Through telephone
Sources of secondary Data: The sources of secondary Data are as follows.
1- Govt. organizations 2- Semi- Govt. organizations 3- Through Internet
4- Teaching and research organizations 5- Research generals and newspapers.