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Understanding the fundamental concepts of statistics is an essential part of every student’s education, especially when it comes to distinguishing between a population and a sample.
In statistics education, a population refers to the entire group about which you want to draw conclusions. A sample, on the other hand, is a subset of the population that is used to represent the larger group. Knowing how to differentiate between these two is crucial, as it influences how results can be generalized and what statistical methods should be employed. For example, if we consider the exercise where an angler records the weight of 12 trout to estimate the size in a lake, a student needs to realize that the 12 trout represent only a sample, not the entire population of the lake’s trout.

Data collection is a systematic process of gathering and measuring information on targeted variables. In our case, the targeted variable is the weight of the trout. There are many ways to collect data, and the method used should align with the research objectives.
The angler's approach in the exercise is a form of primary data collection where he directly gathers information from the source—trout he catches. This is often a starting point in the research process. It's imperative that students understand the scope and limitations of the data they collect. Since the angler collected data on only 12 trout, one must be cautious about drawing broad conclusions about the entire trout population in the lake. This brings to light the critical concept of sample size and its adequacy for making inferences about a population.

There are a variety of sampling techniques used to select a sample from a population, each with its own merits and potential biases.

Simple Random Sampling

In this method, every member of the population has an equal chance of being chosen. It requires a comprehensive list of the population, which wasn't available to the angler.

Systematic Sampling

This involves selecting subjects at a regular interval from an ordered list, which was not used as the angler was catching the trout at random.

Stratified Sampling

Here, the population is divided into strata, and the samples are taken from each stratum. The angler could potentially have used this if he categorized the lake by area.

Convenience Sampling

This is where samples are taken based on ease of access. The angler seems to have used this method, catching whatever trout came his way without a systematic approach.
Different methods come with different levels of reliability for the data collected, and understanding these techniques is vital for critiquing and conducting studies.