Chapter-1 Introduction to Statistics.pdf
- 3. Statistics is concerned with scientific methods for collecting, organizing, summarizing, presenting and analyzing data as well as deriving the valid conclusion and making reasonable decision on the basis of this analysis. The word ‘ Statistics’ is used to refer to - Numerical facts, such as the number of people living in particular area. -The study of ways of collecting, analyzing and interpreting the facts.
- 4. Statistics can be classified into two parts I. Theoretical Statistics or Mathematical Statistics II. Applied Statistics Theoretical or Mathematical Statistics It is application of mathematics to Statistics. It involves collection of facts and analysis of facts using mathematical techniques. It is divided into two parts; a) Descriptive Statistics b) Inferential Statistics
- 5. Statistics which deals with collection of data, presentation of data using table, diagram, graph etc and summarize data using measures of central tendency and measures of variability (spread). Hence summarized results is obtained from descriptive statistics which can describe the data but can not be used to generalized.
- 6. Statistics which deals with sample selection from population and statistical techniques used to draw the valid conclusion about population on the basis of statistical measures obtained from sample. With the help of inferential statistics, one can generalized the results for the whole population by computing statistical measures from the sample. Hence, inferential statistics possess the generalizability capacity and it plays a vital role in statistics.
- 7. Statistics which deals with the application of statistical methods to specific problem is called applied statistics. The statistical tools and methods are used in order to solve many more practical problems in diversified area like computer science, information technology, physics, biology, astronomy, sociology, psychology, business, economics and so on.
- 8. Despite its power, essential usefulness and universal applicability statistics has its own limitation. Some of these limitations are as follows: I. Statistics deal with groups and aggregates only. II. Statistics does not deal with qualitative characteristics directly. III. If sufficient care is not exercised in collecting, analyzing and interpreting the data, statistical results might be misleading.
- 9. IV. Only a person who has an expert knowledge of statistics can handle statistical data efficiently. V. Some errors are possible in statistical decisions. In particular, inferential statistics involves certain errors. We do not know whether an error has been committed or not.
- 11. Measurement is a process of assigning numbers or symbols to any facts or objects or products or items according to some rule. Scale is simply a range of levels or numbers used for measuring something. Different measurements scales are used on the basis of nature of the data. There are generally four type of measurement scales, which are as follows; I. Nominal Scale II. Ordinal Scale III. Interval Scale IV. Ratio Scale
- 12. Nominal Scale It is the lowest level of measurement scale. It is simply a system of assigning numbers or the symbols to objects or events to distinguish one from another. The symbols or the numbers have no numerical meaning so that the arithmetic operations can not be used for these numbers. Categorical data are generally measured on nominal scale. For example ; gender, religion, occupation are measured in nominal scale. If we use 1 for male and 2 for female for measuring gender, then 1 and 2 have no numeric meaning.
- 13. Ordinal Scale When the quantification of observation is done by ranking based on the certain criterion or priorities or importance, then they are said to be measured on an ordinal scale. It represents the qualitative values in ascending or descending order. For example, symptoms of depression from psychiatric assessment such as none is coded by ‘0’, mild ‘1’, moderate’2’, severe’3’. These numbers are known as ranks.
- 14. Interval Scale Some measurement scales possess a constant interval size, they are called interval scale. It assumes data have equal intervals. This scale does not have absolute zero but only arbitrary zero. Scale of temperature is an example of ordinal scale.
- 15. Ratio Scale Ratio scale is the ideal scale and extended form of the interval scale. It is the most powerful scale of measurement. It possesses the characteristics of nominal, ordinal and interval scale. Ratio scale has an absolute zero or true zero point that indicates the completely absence of that property of an object what is being measured. For example, length, weight, age, income, sales etc are measured in ratio scale.
- 16. In statistics, variable may be defined as an attributes that describe person, place, thing or idea under study. And is denoted by capital letters like X, Y, Z etc. It is called a variable because the value may vary between data units in a population, and may change in value over time. For example, age, height, weight of persons life time of any electronic appliance, time to download any image file through internet etc. Generally, variables is classified into two types; I. Qualitative variables II. Quantitative Variable
- 17. Qualitative Variable The variable which varies in kind rather than in magnitude is called qualitative variable. It can be divided into different categories. It is also called categorical variable. Qualitative variable are presented in nominal and ordinal scales. For example, hair color, eye color, gender, smoking habit, etc.
- 18. Quantitative Variable The variable which varies in magnitude and can be expressed numerically is called quantitative data. Quantitative variables are presents in interval and ratio scale. Quantitative variable can be further divided into two types; I. Discrete Variable II. Continuous Variable
- 19. I. Discrete Variable : A variable is said to be discrete if it takes only whole number. For example no. of girls in a class, family size, etc. II. Continuous Variable : A variable is said to be continuous if it takes all possible real values( whole number as well as fractional values) within a certain range. For example, height, weight, age, temperature etc.
- 20. In any statistical investigation first approach is to collect data. It is a set of values obtained on one or more characters under study. It is the collected information which is ready to use for statistical analysis. There are mainly two types of data on the basis of collection procedures; I. Primary data II. Secondary data
- 21. Primary Data : The data which are originally collected by investigator or researcher for the first time with the purpose of statistical inquiry is called primary data. It is collected by government, an individual, institution and research bodies. It needs more fund, time and manpower.
- 22. Following are the method of collecting primary data; Direct personal interview method. Indirect personal interview method. Information through correspondence. Mailed questionnaire method. Schedule through enumerators.
- 23. Secondary Data : The data that has been already collected for a particular purpose and used for next purpose is called secondary data. When investigators find impracticable to collect firsthand information on related issues, secondary data is used. It saves time, money and manpower. Source of Secondary data : I. Published Source II. Unpublished Source
- 24. Published Sources : Different published source of secondary data are national organizations and international agencies. – International agencies such as WHO, World bank, International Labor Organization. – Governmental organizations such as Central Bureau of Statistics, Ministry of Commerce and Industry, Nepal Rastra Bank, Ministry of Finance. – Semi-governmental organizations such as Nepal Food Corporation, Nepal Electricity Authority. – Private organizations such as Nepal Chamber of Commerce, Federation of Nepal Chamber of Commerce and Industry, Publications.
- 25. Unpublished Sources : – Records maintained by government offices. – Records maintained by research institutions, research scholars etc. – Records updated by the departments, institutions for their internal purpose.
- 26. Cross- Sectional data refers to data collected by observing many subjects at the one point or period of time. It is a snapshot of observation at a particular point. For example; Population of women in census year 2068. The data which can be recorded over different periods of time is called time series data. In this case same measurements are recorded on regular basis. For example; population of Nepal in census year 2048, 2058, 2068.
- 27. The data of each unit is recorded for each follow up time till the occurrence of an event or till the unit fails is called failure time data. It is also called time to event data. Time to event data is mostly found in life time analysis of different parts of computers, different software, different industrial products, life time of infrastructure, clinical studies, etc.
- 28. It is a dataset in which the behaviors of entities are observed across time. These entities could be individuals, states, companies, institutions, Countries, etc. Panel data is also known as longitudinal or cross- sectional data. Data of individual is recorded repeatedly over number of years. Income of persons X and Y in years 2014, 2015& 2016 according to age and qualification.
- 29. A population can be defined as an aggregate observation of subjects grouped together by a common feature. Population is the entire pool from which a statistical sample is drawn. Census survey is conducted to enumerate all the population units. Based on the number of individuals belonging to the group, population can be divided into two types; I. Finite population II. Infinite Population
- 30. Based on the type of individuals in population, population can be divided into two types I. Homogeneous Population Population consisting of individuals of same type is called homogeneous population. II. Heterogeneous Population Population consisting of individuals of different type is called heterogeneous population.