#1 Introduction to statistics
- 2. • Statistics is an old science, originated during Mahabharat. • The word ‘statistics’ is known to have been used for the first time in “Elements of Universal Erudition” by Baron J. F. • Webster defined statistics as the classified facts representing the condition of the people in a state, especially those facts which can be stated in numbers or in tables of numbers or in any tabular or classified arrangement.
- 4. According to A. L. Bowley Statistics is the : • Science of counting • The science of averages • The science of measurement of social phenomena, regarding as a whole in all its manifestations. • A subject not confined to any one science. According to A. L. Boddington Statistics is the science of estimates and probabilities.
- 5. According to Croxton and Cowden: Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data. According to Horac Secrist Statistics is an aggregate of facts affected to a marked extent by the multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner foe a predetermined purpose and placed in relation to each other. According to R. A. Fisher The science of statistics is essentially a branch of applied mathematics and may be regarded as mathematics applied to observational data
- 6. Note: • Statistics deals with data, not with simple numbers. • In singular sense statistics means the subject of statistics in which we study various statistical techniques for the analysis of data. • In plural sense statistics means numerical statements about the facts which are capable of analysis and interpretation. • Statistical methods or techniques are applicable only when some data are available irrespective of data collection.
- 7. Data • Data is defined as observations related to some variables. Note:7,2,13,12.5,18 is not a data. As the numbers has no variable related to them but if we say 7,2,13,12,15 and 18 is the age of 6 students then it will the data. Data Quantitative data EXAMPLE: Age, weight of students Qualitative data The data in this case will be quantified by using techniques like ranking, scoring, scaling or coding. EXAMPLE: students in a University --From UG ,PG or Ph. D. --Boy or girl --From UP, Uttarakhand, Kerala, Delhi etc.
- 8. Characteristics of data • Numerically expressed • Aggregates of facts • It should be comparable • It should be conducted in definite systematic manner. • Collected with a definite objective.
- 9. Functions of statistics 1. Collection of data. The data are collected either by experiments or by survey methods (directly or indirectly) 2. Tabulation of data Means preparation of tables in which the classified information can be summarized. It contains number of rows, no. of columns, table number and suitable title of the tables. 3. Analysis of data For analysis of data we apply various statistical techniques e.g.: mean, mode, median, standard deviation, correlation, regression and testing of hypothesis. Question : Two varieties A and B, having mean and SD of Variety A : 75&72 and Variety B :15&4 . Which variety is better.?? 4. Interpretation of data Once the data have been analysed , the main job consist of attaching physical meaning and giving interpretation to the numerical results useful in real life. Answer: Variety B is better because less variation in risk, as S.D. is 4
- 10. Functions contd… Statistics presents the facts in a definite and systematic form. It helps in comparison of different data set. For e.g. we compare average marks of students inn different sections or average yield of different varieties. It helps in finding relationship between various factors For e.g. relationship between weight and B.P. or relationship between quantity of fertilisers and yield. Above relation can be find out with the help of correlation and regression analysis. It helps in formulation of hypothesis and testing of hypothesis. For statistical analysis of data in any research problem first we have to formulate hypothesis It helps in planning. It helps in forecasting.
- 11. Limitations Statistics does not deals with single observation value. It does not deal to qualitative characters e.g. honesty. (however we can analyse the qualitative information by giving some score according to some predefined criteria). Statistical results are true only on an average. Statistics statements or conclusions are generally not true or applicable to individuals but are applicable to majority of the cases.
- 12. Application Statistics is used almost in all the fields . E.g. in Agriculture, veterinary science, engineering ,economics etc.