Non-random sampling, also known as non-probability sampling, is a method where samples are selected based on subjective judgment rather than random selection. Because not every member of the population has a known or equal chance of being included, it is distinct from probability sampling methods.

Quota, judgment, and convenience sampling are all forms of non-probability sampling. In these methods, the selection of units is not based on a known, non-zero probability of inclusion for every member of the population. Instead, they rely on the subjective judgment of the researcher or the accessibility of the subjects, making them non-random techniques.

A census involves collecting data from every single member of a population. For administrative tasks like creating a voters list, where every eligible individual must be accounted for to ensure democratic participation, a complete enumeration (census) is necessary rather than a sample.

A sample is a carefully selected subset of the population intended to represent the characteristics of the whole. The goal of sampling is to ensure that the findings derived from the sample can be generalized to the entire population with a known margin of error. A representative sample is crucial to avoid bias and ensure the validity of statistical inferences made about the population.

Sampling without replacement means that once an element is selected for the sample, it is removed from the population and cannot be chosen again. This process changes the probability of selection for the remaining units in subsequent draws, which is a key consideration in finite population sampling theory.

The regression method of estimation utilizes auxiliary information to improve the precision of population parameter estimates. When a strong linear relationship exists between the auxiliary variable and the variable of interest, the regression estimator typically yields a smaller variance compared to a simple random sample estimator, thereby increasing efficiency.

While surveys are fundamentally about data collection, the provided answer suggests a focus on mathematical calculations. This may refer to the inferential process where survey data is processed to derive population parameters. Note: This answer is unconventional as surveys are primarily for data gathering, not just calculation.

The regression method of estimation uses auxiliary information correlated with the variable of interest to improve the precision of the population mean or total estimate. By reducing the sampling variance of the estimator, it achieves higher precision compared to simple random sampling without auxiliary information.

A population census is defined by the complete enumeration of every individual within a defined population. Unlike a sample survey, which collects data from a subset to make inferences about the whole, a census aims to gather data from every single member of the population to provide a comprehensive count.

Sampling is the statistical procedure of selecting a representative portion of a population. By analyzing this subset, researchers can make inferences about the parameters of the larger population without needing to collect data from every single individual, which is often impractical or costly.