Census and Sampling Methods
Class 11 Statistics — Population vs Sample, Census, Sampling, Sample Size Factors, Requisites, and Comparison
Population vs Sample — The Foundation
Example: If we want to study the average monthly wages of all the 600 workers in a factory, then 600 workers constitute the universe or population.
Under Census Method: collect data from each worker → total of monthly wages of all 600 workers ÷ 600 = average. Under Sampling Method: select few workers (say 60) → total of monthly wages of 60 workers ÷ 60 = average. The sample average can reasonably represent the population average.
Census Method
Key Takeaways
- Highly trained investigators are needed to maintain a high degree of accuracy.
- Demographic data on birth and death rates, literacy, workforce, life expectancy, size and composition of population are collected and published by the Registrar General of India.
- ⭐ Famous example: Census of India conducted after every 10 years. Last Census: 2011. Census 2021 postponed due to COVID-19.
Merits
- Intensive study: Provides intensive and in-depth information covering many facets.
- High accuracy: Since every item is observed personally, highly accurate and reliable information is possible.
- Suitability for non-homogeneous populations: Suitable when different items of the population are not homogeneous.
Demerits
- ✗Expensive: Very expensive especially in case of large population.
- ✗Needs more time and manpower: Large volume of data requires more time and manpower for collection, analysis and interpretation.
- ✗Inapplicability: Cannot be applied in case of infinite population. If study involves destruction (like testing tyres), census cannot be conducted.
Sampling Method
Example: An investigator interested in monthly expenditure in a school of 5,000 students may take a sample of 500 students to record evidence of the whole population.
Factors Affecting Size of Sample
Requisites of a Good Sample
Merits and Demerits of Sampling Method
Merits
- Reduced Cost: More economical than census as collection and analysis is confined to a fraction of the population.
- Greater Speed: Smaller volume of data saves time in collection, processing, editing and analysing.
- Greater Accuracy: When conducted scientifically, gives more accuracy than census. Smaller scale allows well-trained investigators.
- Greater Scope: Possible where highly trained investigators or specialized equipment are limited in availability.
- Administrative Convenience: Low scale of operation makes planning, organisation and supervision convenient.
- Scientific Approach: More scientific than census — possible to determine reliability of results.
- Detailed Enquiry: Small number of units allows collection of detailed and in-depth information.
- Exceptional Applicability: Only alternative when population is infinitely large, spread over large area, or destruction is involved.
Demerits
- Difficult to achieve 100% accuracy: Conclusions based only on a sample — 100% accuracy not possible.
- Lack of Representativeness: Very difficult to obtain a sample truly representative of all characteristics of the population.
- Bias in Selection: Biased investigator may deliberately select a non-representative sample.
- Lack of Specialized Knowledge: Requires particular level of specialized knowledge. Without experts, results are unsatisfactory.
- Not possible for heterogeneous population: If population units are not similar, sample may not correctly reflect characteristics.
Comparison — Census vs Sampling
| Aspect | Census Method | Sampling Method |
|---|---|---|
| Nature of Enquiry | Extensive enquiry — each and every unit of the population is studied. | Limited enquiry — only few units of the population are studied. |
| Economy | Requires large amount of money, time and labour. | Relatively less money, time, and labour required. |
| Suitability | More suitable if population is heterogeneous in nature. | More suitable if population is homogeneous in nature. |
| Reliability and Accuracy | Results are quite reliable and accurate. | Results are less reliable and accurate. |
| Nature of error | Only error of bias may arise. | Error of sampling apart from error of bias. |
| Organisation and Supervision | Very difficult to organise and supervise. | Comparatively easy to organise and supervise. |
Exit Polls
During elections, news channels provide election coverage and predict results through exit polls. Under exit poll, a random sample of voters who exit the polling booths are asked whom they voted for. From the data of the sample of voters, the prediction is made.