Answer: Errors in sample surveys arise mainly due to two broad causes — sampling errors and non-sampling errors . Understanding these errors is crucial for improving the accuracy of survey results. 1. Sampling Errors: Sampling errors occur because only a sample, not the entire population, is studied. Different samples can yield slightly different estimates, even when drawn from the same population. Examples of Sampling Errors: Different samples may provide varying average i

📋 What makes a good Sampling Frame, and why is it important? Answer: A sampling frame  is the complete list of all population units from which a sample is drawn. A good sampling frame  ensures that every unit of the target population has a chance to be selected. Characteristics of a Good Sampling Frame: Completeness: Includes all units of the target population (no omissions). Accuracy: Information (names, addresses, IDs) should be correct and updated. Uniqueness: Each unit

🧩 What are the key steps involved in designing a Sample Survey? Answer: Designing a good sample survey is a systematic process . Each step ensures reliability and accuracy of results. Main Steps: Define the Objective: Clearly state what you want to estimate — e.g., average income, literacy rate, unemployment level. Define the Target Population: Specify the group about which information is required (e.g., all households in Delhi, or all workers in manufacturing). Prepare the

📊 Why do we prefer Sampling in large-scale statistical investigations? Answer: Sampling is preferred in large-scale investigations because it provides quick, economical, and practical  results without compromising reliability. Main Reasons: Economy of Resources: Conducting a census on millions of units requires huge manpower, cost, and time. Sampling reduces this burden. Speed: Sampling allows faster data collection and analysis — critical when decisions are time-sensitive (

🎯 What is the basic difference between a Census and a Sample Survey? Answer: A Census  is a complete enumeration of every individual or unit in the population. It collects information from 100% of the population .A Sample Survey , on the other hand, collects information only from a subset of the population  (a sample), and uses statistical inference to estimate characteristics of the entire population. Key Differences: Basis Census Sample Survey Coverage Entire population S

📉 If two different samples of the same size from a population give very different results, what might be the reason? Answer: This situation occurs when sampling variability  or non-sampling errors  are high. Possible Reasons: High Sampling Variability: Population is highly heterogeneous. Sample size nnn is too small. Sampling method is inefficient. Mathematically, sampling variance Improper Sampling Method: Non-random or biased selection. Poor stratification or incomplete sa

🧾 Q. Explain how you would conduct a Pilot Survey before final sampling. Answer: A Pilot Survey  (or Pre-test ) is a small-scale trial survey conducted before the main survey to test the feasibility, clarity, and reliability of the questionnaire, sampling plan, and field procedures. Steps Involved: Objective Definition: Clarify what aspects need testing — questionnaire wording, time per interview, response rate, etc. Sample Selection: Choose a small but representative area o

🏘️ In a village with 5 wards, you are to select 2 wards and then 10 households from each. What sampling design is this? Answer: This is a Two-Stage Sampling Design  (a specific form of Multistage Sampling ). Explanation: Stage 1 (Primary Stage): Select 2 wards out of 5 using Simple Random Sampling Without Replacement (SRSWOR) . Each ward acts as a Primary Sampling Unit (PSU) . Stage 2 (Secondary Stage): Within each selected ward, list all households and select 10 households

🧠 Suppose you are asked to estimate the average household income in Delhi. Which sampling method would you use and why? Answer: To estimate average household income in Delhi , the best design would be Stratified Multistage Sampling. Step-by-Step Explanation: Stratification: Delhi’s population is heterogeneous — it varies by region (North, South, East, West, Central), income level, and urban density.Therefore, we divide it into strata  based on region or socioeconomic categ

🧠 What is Multistage Sampling? Answer: Multistage Sampling  is an extension of cluster sampling where sampling is carried out in two or more stages . Example: First Stage:  Select districts (Primary Sampling Units). Second Stage:  Select villages within districts. Third Stage:  Select households within villages. At each stage, sampling can be SRS, systematic, or stratified depending on design. Advantages: Suitable for large-scale and geographically dispersed populations. Sa

🏘️ What is Cluster Sampling? Answer: In Cluster Sampling , the population is divided into natural groups (clusters)  such as villages, schools, or wards. A few clusters are randomly selected, and all or some units within selected clusters  are studied. Advantages: Economical and operationally feasible for large areas. Reduces cost of travel and listing. Disadvantages: Less precise due to homogeneity within clusters (high intra-class correlation). Requires adjustment for clu

🔢 Explain Systematic Sampling. Answer: In Systematic Sampling , units are selected at regular intervals  after a random start. If population size = N and sample size = n, then sampling interval  k=N/n. Select a random number r between 1 and k. The sample consists of: r, r+k, r+2k, …, r+(n−1)k Advantages: Simple and quick. Ensures even coverage across population. Suitable when list is arranged in an order (e.g., households in a street). Disadvantages: Can lead to bias if popu

🧩 Define Stratified Sampling. Answer: In Stratified Random Sampling , the population is divided into homogeneous subgroups (strata)  based on certain characteristics (like region, gender, income group), and random samples  are drawn independently from each stratum. Types of Allocation: Equal Allocation ​ Proportional Allocation Optimum (Neyman) Allocation Advantages: More precise than SRS (reduces sampling error). Ensures representation of all key subgroups. Allows separate

📊 Explain Simple Random Sampling (SRS). Answer: Simple Random Sampling (SRS)  is the most basic probability sampling technique in which every unit of the population has an equal and independent chance  of being selected in the sample. Two methods exist: SRSWR (With Replacement)  – a unit, once selected, is replaced before the next draw. SRSWOR (Without Replacement)  – a unit, once selected, is not replaced. ​ Advantages: Easy to understand and apply. Provides unbiased estima

🎯 What is Sampling Error? How does it differ from Non-Sampling Error? Answer: Sampling Error: It arises because only a part (sample) of the population is studied. Different samples drawn from the same population will give slightly different estimates.✅ Can be reduced by increasing sample size or using efficient designs. Non-Sampling Error: It arises from causes other than sampling, such as: Measurement error Response bias or non-response Wrong data entry or tabulation Inte

🎯 Define ‘Sampling Frame’. Answer: A sampling frame  is the complete list or database of all units in the target population from which the sample is actually drawn. It acts as a bridge between the theoretical population  and the sample . Examples: Voter list → sampling frame for election survey. School register → sampling frame for student survey. List of villages from Census → frame for rural surveys. Cross Question: What happens if the sampling frame is incomplete or out

🎯 What are the Main Types of Sampling Methods? Answer: Sampling methods are broadly classified into two categories: A. Probability Sampling (each unit has a known chance of selection): Simple Random Sampling (SRS)  – every unit has equal chance. Systematic Sampling  – every kᵗʰ unit is selected after a random start. Stratified Sampling  – population divided into strata; random sample from each. Cluster / Multistage Sampling  – groups or clusters are randomly selected, then u

🎯 Why do we prefer Sampling over Complete Enumeration? Answer: Sampling is preferred because: Economical:  It saves time, money, and manpower. Practical:  Sometimes, it’s physically impossible to collect data from every individual (e.g., soil testing, manufacturing quality tests). Speed:  Enables quicker decision-making. Accuracy in Practice:  With trained investigators and good design, sampling often gives more reliable results than a poorly conducted census. Example: In q

🎯 What is Sampling? Answer: Sampling is the process of selecting a subset of individuals or units (called a sample ) from a larger group or population to draw conclusions about the entire population. Since studying the whole population (called a census ) is often expensive, time-consuming, or impractical, sampling provides a way to estimate population parameters like mean, proportion, or variance using statistical inference. Example: If we want to estimate the average house

Gandhi Jayanti, celebrated on October 2nd, marks the birth anniversary of Mahatma Gandhi, a crucial figure in India's fight for...