Statistics: meaning, scope, limitations and collection of data

1. Meaning and definitions

The word is used in two senses. In the plural sense, statistics means numerical facts: the population of a district, the monthly sales of a firm, the wholesale prices of rice. In the singular sense, it means the science of collecting, organising, presenting, analysing and interpreting such facts.

• A.L. Bowley: “Statistics may be called the science of counting”; and elsewhere, “the science of averages.” Both are too narrow: counting and averaging are only parts of the method.
• Croxton and Cowden: “Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.” This is the best short definition of statistics as a method, because it names the four stages.
• Horace Secrist: statistics are “aggregates of facts, affected to a marked extent by a multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose, and placed in relation to each other.” This is the standard definition of statistics as data.

2. Characteristics (from Secrist’s definition)

1. Aggregates of facts. A single figure (one man’s height) is not statistics; a series of figures is.
2. Affected by many causes. Crop output depends on rain, seed, fertiliser and labour together.
3. Numerically expressed. “Sales were good” is not statistics; “sales rose from Rs. 40 lakh to Rs. 52 lakh” is.
4. Enumerated or estimated with reasonable accuracy. Small fields can be counted; large ones (crowd at a rally) are estimated.
5. Collected systematically for a pre-determined purpose.
6. Placed in relation to each other, so that they are comparable (same units, same period, same definitions).

3. Functions

• Presents facts in a definite form — numbers are more convincing than vague statements.
• Simplifies complex data through averages, percentages, tables and diagrams.
• Facilitates comparison (coefficient of variation, index numbers).
• Helps in formulating and testing hypotheses (does advertising raise sales?).
• Helps in forecasting (regression, trend).
• Helps in policy-making by government and firms.
• Enlarges individual knowledge and experience.

4. Scope (importance in different fields)

• Business and management: market research, sales forecasting, quality control (control charts), inventory planning, fixing prices.
• Economics: national income estimation, cost of living and price indices, demand and supply analysis.
• Government and administration: the Census, budgeting, planning, fixing dearness allowance from the consumer price index.
• Banking and insurance: deposit and credit trends, mortality tables for fixing premiums.
• Accounting and auditing: sampling in audit, cost analysis.
• Law: crime statistics, judicial pendency data, evidence of discrimination by comparing groups.
• Natural and social sciences: medicine (clinical trials), sociology, psychology (intelligence tests).

5. Limitations

1. Studies aggregates, not individuals. The average income of a village says nothing about a particular villager.
2. Deals with quantitative facts only. Honesty, beauty and loyalty cannot be measured directly; they must be converted into ranks or scores.
3. Results are true only on average. Statistical laws are not exact like the laws of physics.
4. Can be misused. Data can be selected or presented to prove a desired conclusion, hence the saying (popularised by Mark Twain) about “lies, damned lies and statistics”.
5. Only experts can use it safely. A wrong average or a non-comparable base gives a wrong conclusion.
6. Data must be uniform and homogeneous. Comparing a firm’s sales in rupees with another’s in units is meaningless.

Distrust of statistics arises from these limitations, not from the science itself. The remedy is careful collection and honest interpretation; as is often said, statistics are like clay, from which one can make a god or a devil.

6. Collection of data: primary and secondary

Primary data are collected for the first time by the investigator for the purpose in hand; they are original. Secondary data have already been collected by someone else and are used by the investigator for his purpose.

Sources of secondary data. Published: government reports (Census, MoSPI, RBI Bulletin, Economic Survey), international bodies (IMF, World Bank, UN), trade journals, company annual reports, research publications. Unpublished: records of firms, theses, private files.

Before using secondary data, check reliability (who collected it, by what method), suitability (same definitions, units, period) and adequacy (enough coverage).

7. Methods of collecting primary data

1. Direct personal investigation. The investigator meets the informants himself. Accurate and flexible, but suitable only for a small, local field; costly and open to the investigator’s bias.
2. Indirect oral investigation. Information is obtained from third persons (witnesses) who know the facts, as in commissions of inquiry. Covers a wide field, but accuracy depends on the witnesses.
3. Information through local sources or correspondents. Local agents send estimates periodically (used by newspapers and for crop reports). Cheap and continuous, but not very accurate.
4. Questionnaires sent by post (mailed questionnaire). Covers a wide area cheaply, but works only with literate informants and suffers from non-response.
5. Schedules filled by enumerators. Trained enumerators visit the informants and fill in the schedule themselves (the Census method). Works with illiterate informants and gives good response, but is expensive and needs training.

A good questionnaire is short, has simple and unambiguous questions, avoids personal and leading questions, follows a logical order, uses closed (yes/no, multiple choice) questions where possible, gives instructions, and is pre-tested on a small group (a pilot survey).

How this is examined

“Define statistics. Explain the scope and limitations of statistics” (January 2025, and the 100-mark January 2026 paper); “Discuss the scope, functions and limitations of statistics” (January 2026); “Define statistics. Explain the characteristics of statistics” (August 2024); “Explain the limitations of statistics” as a six-mark note (August 2024). On data: “What is primary data? Explain the various methods of collecting primary data” (June 2025) and “Distinguish between primary and secondary data” (January 2025). For a ten-mark answer, give two definitions, then use the numbered headings above with an example under each.