ISS 2016 Statistics Paper-1 Solution: Question 40 (Sampling Frames for Wildlife Populations)
This post continues our ongoing question-by-question walkthrough of the ISS Statistics Paper-1 previous year papers. We are currently working through the 2016 paper in strict serial order, and today we tackle Question 40, which tests a concept that trips up a surprising number of aspirants: the difference between a population and a sampling frame.
Quick Summary
Topic: Sampling theory — construction of sampling frames for mobile/wildlife populations
Question Reference: ISS 2016, Statistics Paper-1, Question 40
Correct Answer: Option (a) — Both Statement I and Statement II are true, and Statement II is the correct explanation of Statement I
The Question as It Appeared in the Paper
Consider the following statements:
Statement I:It is not possible to determine the total number of birds in a forest by standard sampling technique.
Statement II:It is not possible to construct the sampling frame for such populations.
Which one of the following is correct in respect of the above two statements?
Both Statement I and Statement II are true and Statement II is the correct explanation for Statement I.
Both Statement I and Statement II are true but Statement II is not the correct explanation for Statement I.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Step 1: Understand What Kind of Question This Is
This is an assertion-reason style question, even though it is phrased as "Statement I" and "Statement II" rather than "Assertion" and "Reason." There are really three separate things you must check, one at a time, before you can pick an option:
Is Statement I true on its own?
Is Statement II true on its own?
If both are true, does Statement II actually explain why Statement I is true, or are they just two unrelated true facts sitting next to each other?
Skipping the third check is exactly how students lose marks on this type of question, even when they know the underlying statistics perfectly well.
Step 2: What Is a Sampling Frame?
Before we can judge Statement II, we need to be precise about what a sampling frame actually is. A sampling frame is a complete, physical list (or a well-defined device for generating one) of every sampling unit in the population, from which units are then selected using a probability sampling scheme such as simple random sampling, systematic sampling, or stratified sampling.
For example, if your population is "all registered voters in a district," the electoral roll is your sampling frame. If your population is "all households in a village," a household listing prepared during a census operation is your frame. In both cases, every unit in the population can, in principle, be written down, numbered, and selected with a known, calculable probability.
Step 3: Can You Construct a Sampling Frame for Birds in a Forest?
Now apply the same test to "all birds in a forest." Try to imagine actually building the list:
Birds are not individually registered or tagged in advance, so there is no master list to start from.
Birds move continuously, across territories and often across the boundary of the forest itself, so even a list built today would be wrong by tomorrow.
You do not know, and cannot know in advance, how many birds exist in total — which is precisely the quantity the sampling exercise is trying to estimate. You cannot build a frame that depends on the answer you have not yet found.
Because none of these three conditions can be satisfied, it is genuinely impossible to construct a sampling frame for a population like birds in a forest. So Statement II is true.
Step 4: Is Statement I True, and Does It Follow From Statement II?
Every standard sampling technique taught in a first course in sampling theory — simple random sampling, systematic sampling, stratified sampling, cluster sampling — shares one non-negotiable requirement: you must be able to list, number, or otherwise enumerate the units of the population before you can draw a probability sample from it. That list is exactly the sampling frame.
Since Step 3 established that no such frame can be built for birds in a forest, it follows directly that none of the standard sampling techniques can be applied to determine their total number. So Statement I is also true, and more importantly, it is true because Statement II is true. The absence of a frame is not a coincidental fact sitting beside the difficulty of counting birds — it is the actual mechanical reason the standard techniques break down.
Pro Tip: The trap in this question is not figuring out whether the statements are true — most students get that part right. The trap is deciding whether option (a) or option (b) applies, i.e., whether Statement II truly
Step 5: What Do You Actually Use Instead?
This question is also testing whether you know what statisticians do when a sampling frame genuinely cannot be built. For elusive or mobile populations such as birds, fish, or wild animals, the standard alternative is the capture-recapture method (also called the mark-recapture or Lincoln-Petersen method). In its simplest form: capture and mark a sample of n1 individuals and release them; later, capture a second sample of n2 individuals and count how many,m, are already marked. The total population size is then estimated as
N̂ = (n1 × n2) / m
This technique sidesteps the need for a sampling frame entirely — it never requires a pre-existing list of the population, only two successive samples and the overlap between them.
Final Answer
Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I. This matches option (a), which is also what the official answer key (Series A) confirms for Question 40 — so our derivation and the official key agree with no discrepancy.
Why This Question Matters
Sampling frame construction is one of the most practically important ideas in applied sampling theory, because it determines whether a standard design-based method can be used at all. Questions like this one check whether a candidate actually understands the preconditions for simple random sampling and its relatives, not just the formulas for mean and variance under those designs. In real survey and ecological work, recognizing when a frame cannot be built — and knowing that specialized techniques like capture-recapture exist for exactly that situation — is a genuinely useful skill, not just an exam trick.
Frequently Asked Questions
What exactly is a sampling frame in statistics?
A sampling frame is the complete, enumerable list or device that identifies every unit in the population you want to study, used as the basis for drawing a probability sample. Without it, you cannot assign a known selection probability to each unit, which is required for standard techniques like simple random sampling.
Why can't we just estimate the number of birds using a simple random sample?
Simple random sampling requires selecting units at random from a pre-built list of all units in the population. Since birds cannot be pre-listed, individually identified in advance, or kept stationary, there is no frame to sample from, so simple random sampling cannot be applied directly to this problem.
What method is actually used to estimate wildlife population sizes?
The capture-recapture (mark-recapture) method is the standard approach. It estimates total population size from the overlap between two successive samples of marked and unmarked individuals, and it works precisely because it does not require a sampling frame.
How do I tell the difference between option (a) and option (b) in this type of question?
Check whether the second statement is the actual mechanical cause of the first, not just another true fact about the same topic. A useful test is to ask whether the first statement would stop being true if the second statement were false; if yes, the second statement is the explanation, pointing to option (a).
Are there other real-life populations where a sampling frame cannot be built?
Yes — homeless populations, migratory fish stocks, insect populations, and illegal or hidden populations (such as unregistered workers) all share the same problem: no stable, enumerable list exists, so specialized techniques such as capture-recapture, network/snowball sampling, or indirect estimation methods are used instead of standard frame-based sampling.
Does "no sampling frame" mean estimation is impossible altogether?
No. It only means standard frame-based probability sampling techniques cannot be used directly. Estimation is still possible through alternative, frame-free methods such as capture-recapture, which is exactly the point this question is testing.
If anything here was unclear, or if you solved this one differently, drop a comment below — and if you know a fellow ISS aspirant working through the same previous year papers, feel free to share this post with them.
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