Q.1. Define statistics in singular and plural form. Write down the main features of statistics.
Ans. Singular form: Statistics in the singular refers to the discipline concerned with the collection, presentation, analysis and interpretation of numerical data. Plural form: Statistics in the plural denotes the numerical facts or figures themselves - quantitative data that are usually affected by a multiplicity of causes. Features of Statistics
(i) Aggregate of Facts: Isolated or single values are not regarded as statistics because a single number cannot be related or compared to draw meaningful conclusions. A group or aggregate of figures is necessary for statistics, since only then comparisons and inferences are possible.
(ii) Numerically Expressed: Facts must be expressed in numerical form to be called statistics. Statements in words (for example, "He is tall") are not statistics unless converted into measurable terms (for example, "He is 7 inches taller than his brother").
(iii) Reasonable Standards of Accuracy: Data may be collected either by exact counting or by estimation depending on the scope of the study. For a large population, estimates may be acceptable, while for a small or well-defined group precise counts are preferred.
(iv) Affected by Multiplicity of Causes: Statistical facts are usually influenced by several factors. A datum affected by only one cause cannot be studied as a meaningful statistical aggregate because the combined effects of many causes are typical of statistical observations.
(v) Placed in Relation to Each Other: Data must be comparable and homogeneous to yield useful information. Comparison across incompatible units (for example, the weight of an elephant with that of a human) is meaningless unless suitable adjustments are made.
(vi) Collected for a Predetermined Purpose: Data gathered without a definite objective remain mere figures. Statistics require a clear purpose so that the collected data can be processed and interpreted to answer specific questions.
Q.2. Explain the limitations of statistics.
Ans. Statistics is a valuable tool in modern decision-making, yet it has certain limitations that must be recognised. These limitations are as follows:
(i) Deals with Only Numerical Facts: Statistics deals chiefly with measurable numerical facts. Qualitative qualities such as beauty, attitude or honesty are not directly measurable and must be converted into numbers before statistical methods can be applied.
(ii) Deals with Aggregates Not with Individuals: Statistical results describe groups or averages and do not necessarily reflect the situation of any single individual within the group.
(iii) Possibility of Misleading Results: Statistical conclusions may be misleading if data are taken out of context, if inappropriate measures are used, or if important variables are ignored. Proper interpretation is essential.
(iv) Can Be Misused: Statistics can be manipulated or presented selectively to support particular interests. Misuse may distort public opinion or lead to wrong decisions.
(v) Results Are Only Approximately True: Many statistical studies are based on samples rather than complete enumeration. As a result, findings are subject to sampling error and generally represent approximations rather than exact truths.
(vi) Requires Expertise for Correct Use: Proper collection, analysis and interpretation of statistics demand technical skill. Incorrect methods or poor understanding can produce wrong conclusions, so expertise is often necessary for reliable results.
Q.3. Explain in detail the functions of statistics.
Ans. The main functions of statistics are as follows:
(i) Establishing Relationships Between Variables: Statistics provide tools, such as correlation analysis, to study how one variable changes with another. For example, correlation techniques can show whether income and expenditure move together and whether the relationship is positive or negative.
(ii) Enabling Comparisons: Statistics make comparison possible across time, regions, groups or categories. Without organised data presented in comparable form, meaningful conclusions cannot be drawn.
(iii) Simplifying and Presenting Data Clearly: Statistics transform complex facts into simple, understandable forms. Presentation techniques help users to grasp information quickly. Common techniques used for presentation are:
- Classification
- Averages
- Graphs
- Diagrams
- Percentages
- Ratio
(iv) Condensing Large Masses of Data: Statistics reduce bulky data into concise summaries (for example, averages and indices) that capture the essential information in a compact form.
(v) Forecasting and Planning: By analysing past trends and patterns, statistics help in forecasting future values of economic variables and aid planners and policymakers in decision-making.
(vi) Increasing Knowledge and Supporting Argument: Statistical evidence strengthens understanding, improves expertise and provides objective support for arguments and decisions in academic, business and policy contexts.
