Preface This book is designed especially for under Graduate students of Agriculture and Allied Sciences and has been prepared in consonance with the syllabus recommended by the Fifth Deans Committee. The book would also be immensely helpful to agriculture graduates preparing for JRF and other competitive examinations. The concepts in the book have been analysed and presented in a simple and precise manner to the comprehension of the students. I hope, my sincere endeavour would cater to the needs of the students and render them immense benefit. I thank M/s New India Publishing Agency, New Delhi for taking up the publication of the book in neat, flawless and presentable form. I owe indebtedness, pay profound ovation and dedicate this little effort of mine to my departed parents who always prodded me for academic excellence and dissemination of knowledge.

The word ‘statistics’ has been derived from the Latin Word ‘Status’ which means ‘Political State’. The word statistics has been coined by Gottfried Aschenwall, a German Political Scientist. Ronald Aylmer Fisher is regarded as father of modern statistics. The word statistics has meaning both in plural and singular sense. In plural sense, it means quantitative/qualitative figures. For example, the area under food grains in different states of India, the production of guava in different states of India, germination percentage of seeds, etc.. In singular sense, it means as a subject i.e., method of dealing with the quantitative/qualitative information. Statistics is defined as scientific method which deals with collection, organization presentation, analysis and interpretation of data. It is included under both science and arts. Statistics is used as a tool to obtain knowledge on other subjects of science.

Frequency distribution table is a statistical table which shows the sets of all distinct values of the variables arranged in order of their magnitude either individually or in groups with their corresponding frequencies side by side. Need for frequency distribution table To condense the data To provides quick reference for the entire data To facilitate quick & easy statistical analysis of data To reveal the pattern within the data

Presentation of data is done in form of diagram and graphs. Diagrammatic Presentation: The data are presented in form of diagrams The important diagrammatic presentations are simple bar diagram, multiple bar diagram, component bar diagram, percentage bar diagram & pie diagram. Selection of diagram depends upon the nature of classification, number of characters involved and the type of comparison required to be made. In all the diagrams, the groups or classes are represented on the X-axis and the volumes or frequencies are represented in the Y-axis. The title of these visual aids should be self-explanatory. Simple Bar Diagram: Simple bar diagrams consist of vertical bars of equal width. The height of these bars is proportional to the magnitude of the attribute. All bars are separated from each other by equal intervals. Simple bar diagram is used if the classification is based on attributes and if the attributes are to be compared with respect to a single character. For example, the area under different crops in a state, the production of mangoes in different years for a state, the yield of a variety at different fertilizer level, etc, can be represented by the simple bar diagram. Also the yield performance of different varieties of a crop, the effects of different treatments etc, can be compared using simple bar diagrams.

Measures of central tendency are also known as averages. Averages are defined as statistical constants which enable us to understand in a single effort, the significance of the whole i.e., they are the representative value of the distribution. They give an idea about the concentration of the values in the central part of the distribution. Five Types of Averages Arithmetic Mean It is the sum of all the observations divided by the number of observation. For individual data or simple series (i.e., series in which all values have single frequency)

Literal meaning of dispersion is scatterdness. We study dispersion to have an idea about the homogeneity and heterogeneity of the distribution. Dispersion gives an idea about how much the values of the observation varies from their averages. The series in which the values of the observation differ much from their averages is said to be heterogeneous or highly dispersed. The series in which the value of the observation does not differ much from their averages is said to be homogenous or less dispersed. There are two types of measures of dispersion:

In some experiments the result can be predicted with certainty. For example, the bulb will stop glowing when switched off, the evolution of hydrogen gas when zinc reacts with dilute hydrochloric acid. Such phenomenon where the result can be predicted with certainty is known as deterministic phenomenon. But in some experiments the result cannot be predicted with certainty. For example, Sales of a firm, profit made by a company, yield of a crop, etc. Such phenomenon where the result cannot be predicted with certainty are known as probabilistic or random phenomenon. Such phenomena are frequently observed in economics, business, agriculture, social science, biology, etc., and in our day to day life. The theory of probability is a very important branch of statistics which provides a numerical measure of uncertainty.

Random variable: A random variable is a variable that assumes numerical values associated with the events of a random experiment whose outcomes cannot be predicted with certainty. For example, Height of rice plants in a field; seed weight; No. of tillers per rice plant. A random variable is of two types:- Discrete random variable: The random variable which takes only countable values i.e., integral values. For Example, Number of tillers per rice plant. Here there can be finite no. of values between any two values. Continuous random variables: The random variable which takes values within intervals. These values cannot be counted but can only be measured. Here there can be infinite no. of values between any two values for example, Height of rice plants in field; seed weight.

Concept of correlation was given by Karl Pearson in 1890. The study of strength and nature of relationship between two variables is called correlation. Two variables are said to be correlated, if the change in one variable affects the other variable. Correlation is also known as covariation. Bivariate Distribution: Distribution involving two variables is known as bivariate distribution. For example, Height and weight of persons, yield and production of a crop in. On basis of type of association between variables, correlation is of two types:

The aggregate of data forming a subject of investigation is known as population. Example, All the crop plants grown in a plot; all the fruit plants in an orchard, etc. The population may be: Finite: No. of observations are definite. e.g., number of farms in a village, no. of house in a locality, no. of trees in an orchard are all finite population. Infinite: Number of observation are indefinite e.g., (a) Number of insects in a region, number of grasses in a field etc. are all infinite population. The Population may be: hypothetical or theoretical Hypothetical population consists of unit that has no physical existence. This population exists only in imagination. For example, Result of tossing coin, throwing die, Existent or real population consists of units that are physically present. This population actually exists. For example, Number of employees in a factory, Number of farms in a village.

A sample is said to be small sample if the sample size(n) is less than 30. Various small sample tests are: (i) t-test (ii) F-test t-test performs the following tests for small sample(s). To test the equality between a single sample mean and the assumed population mean. To test the equality of two independent sample means. To test the equality of two paired sample means. To test the equality between sample correlation coefficient and the assumed population correlation coefficient

Samples having size, n - 30 are known as large sample. For large values of n (i.e., for n - 30), almost all the distributions are very closely approximated by normal distribution. Thus in this case we apply the normal test, which is based upon the area property of the normal probability curve. Large Sample Test is also known as Z-test or SND (Standard Normal Deviate) test.

Chi-square test is a non-parametric test as the null hypothesis does not contain any assumption regarding the population parameter. Chi-square is also written as c2. In this chapter two uses of chi-square test will be dealt with. They are the following :

An experiment is a systematic process or activity which leads to collection of information on certain objects to give an answer to the objectives of the researcher. The experiment in which certain absolute values like average, correlation coefficient, median, mode, etc are worked out to describe the population is known as absolute experiment. The experiment in which the effects of different objects under consideration are compared is known as comparative experiment. The variable whose change we wish to study is called as Response variable. For example- yield, mortality rate of insects etc. The variable whose effect on the response variable we wish to study is termed as Factor. For example - variety, fertilizer, insecticide etc. Here factor is the independent variable and response variable is the dependent variable. The various levels of a factor whose effect on the response variable we wish to study are known as Treatment.