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**Q.1. Define statistics in singular and plural form. Write down the main features of statistics. Ans. **Singular form: Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data. Plural form: Statistics mean quantitative data, affected to a marked extent by multiplicity of causes. Features of Statistics

(i) Aggregate of Facts: Isolated and single value is not called as statistics because a single value cannot be related, compared and conclusion cannot be drawn from it. Aggregate of figures is called statistics due to their comparability.

(ii) Numerically Expressed: Any fact expressed in words cannot be called statistics because it does not provide any information. For instance, the statement â€˜He is tallâ€™ is not statistics but â€˜He is 7 inches taller than his brotherâ€™ is statistics as conclusions can be drawn from it.

(iii) Reasonable Standards of Accuracy: Data is collected or can be calculated purely on the basis of calculations or estimates, which depend on the field of investigation. For instance, if the field is wide then collection can be done on the basis of estimate such as 3 lakh people from Himachal Pradesh and 2 lakh people from Punjab participated in Republic Day parade. However, if the field of investigation is small, data can be collected using calculation.

(iv) Affected by Multiplicity of Causes: Data which is affected by single reason cannot be called as statistics. The facts or data which are affected by a number of factors are called statistics. In statistics, effect of independent values on dependent values cannot be separated.

(v) Placed in Relation to Each Other : Comparison of data would be feasible only if the data is homogenous. One cannot compare weight of elephant with that of a human.

(vi) Collected for Predetermined Purpose: Data collected without a purpose are just numbers or information but not the statistics. If we collect data regarding the farmers without deciding any purpose then the data would not be able to derive the required conclusions.

Ans.

(i) Deals with Only Numerical Facts: Statistics studies only numerical facts of a problem. Qualitative aspects such as beauty, gender, attitude, etc. cannot be studied in statistics. In order to study statistics, we need to give a numerical value to qualitative attributes.

(ii) Deals with Aggregates not with Individuals: Statistical data are aggregates of facts and hence, it does not have any place for individual cases.

(iii) Possibility of Misleading Results: There is a possibility to arrive at wrong and misleading conclusions if statistical results are not placed in the proper context.

(iv) Can be Misused: The results obtained from a data can be manipulated according to oneâ€™s own interest. Such manipulated results can misdirect the society.

(v) Results are Only Approximately True: The inferences drawn from statistical analysis are generally approximates. Statistical studies are usually based on sample taken from the universe. Under such circumstances, conclusions are bound to be only approximate.

(vi) Must be used Only by Experts: Since statistics is a technical subject, it is very difficult for an ordinary person to use and apply it. Only experienced and skilled people can make correct use of it and derive right conclusions.

Ans.

(i) Statistical tools help in establishing relation between various variables. Tool used in establishing the relation is known as correlation and method used for analysis using this tool is known as correlation analysis. For instance, statistics can be used to establish relationship between the income and expenditure of a group of 10 people. Relation can be negative or positive.

(ii) Statistics help in doing comparisons. Objective of collecting data is not fulfilled until conclusions are drawn from them, and conclusion could be drawn only when data is comparable.

(iii) Statistics helps in simple and easy presentation of fact and figures. It is a very difficult task for any person to understand and present complicated data. Statistics performs the task of making presentation of data simple and understandable. Following techniques are used in this function of statistics:

- Classification
- Averages
- Graphs
- Diagrams
- Percentages
- Ratio

(iv) Statistics help in giving a definite and condensed form to data.

(v) Statistics are used to undertake forecasting. Statistics related to previous trends of a variable help in predicting the value of the variable in near future.

(vi) Statistics helps in increasing the knowledge, expertise and argumentative power.

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