Population vs. Sample | Definitions, Differences & Examples

Sample

The term “sample” refers to a portion of the population that is representative of the population from which it was selected. Depending on the sampling method, a sample can have fewer observations than the population, the same number of observations, or more observations. More than one sample can be derived from the same population.

So, a sample is a subset of individuals or observations taken from a larger population. The sample is used to make inferences or conclusions about the characteristics or parameters of the population.

Population

The term “population” is used in statistics to represent all possible measurements or outcomes that are of interest to us in a particular study. So, a population is the entire group of individuals or observations that we are interested in studying. The population can be finite, such as all the students in a school, or infinite, such as all the potential customers in a market.

For example, suppose you are interested in studying the average height of all adult women in a particular country. The population would be all adult women in that country, while the sample would be a group of women selected from that population. By analyzing the sample, you can make inferences about the height of the entire population.

It is essential to use a representative sample to ensure that the results accurately reflect the characteristics of the population. A representative sample is one that is randomly selected from the population and adequately reflects the diversity and variability of the population.

Population vs sample

Population	Sample
A population refers to the entire group of individuals or observations that we are interested in studying.	A sample is a subset of individuals or observations taken from the population.
The population size can be finite or infinite.	The sample size is always smaller than the population size.
The parameter of the population is a numerical or measurable element that defines the system of the set.	The statistic is the descriptive component of the sample found by using sample mean or sample proportion
Conducting a study on the entire population can be costly and time-consuming.	While studying a sample can be more practical, economical and efficient.
Inferences about the population are made based on the characteristics of the sample.	While inferences about the sample are made based on the characteristics of the individuals or observations in the sample.

Why Sample Vs Population required for Inferential Statistics?

Statistical inference is the branch of statistics concerned with drawing conclusions and/or making decisions concerning a population based only on sample data.

Let’s consider an awesome example given by great professor. Suppose you are cooking some recipe and you want to test it before serving to the guest to get an idea about the dish as a whole. You will never eat the full dish to get that idea. Rather you will taste very little portion of your dish with a spoon.

• So here you are only doing exploratory analysis to get idea what you cook with a sample in your hand.
• Next if you generalize that your dish required some extra sugar or salt then that making an inference.
• To get a valid and right inference your portion of dish that you tested should be representative of your sample. Otherwise conclusion will be wrong.

Census

Census  attempt to gather information from each and every unit of the population of interest. A census is a complete enumeration or count of a population, typically conducted by a government or other official agency. It involves gathering information on all individuals or entities in a defined geographic area or jurisdiction, such as a country, state, city, or county.

Censuses usually collect demographic, social, economic, and housing data on each individual or household, including age, gender, race, ethnicity, education, occupation, income, and household composition. The collected data is then used for various purposes, such as determining the size and characteristics of the population, assessing social and economic trends, planning and evaluating public services and programs, and apportioning political representation and resources.

Censuses can be costly and time-consuming to conduct, and are often conducted only once every decade or so. In some cases, a sample survey may be used as a less expensive alternative to a full census. However, censuses provide the most accurate and comprehensive information about a population, making them a valuable tool for policymakers, researchers, and other stakeholders.

 

Now the question is why we use sample in statistics why don’t we go for census?

Why using a sample? Why not census?

• Less time consuming than a census;
• less costly to administer than a census;
• measuring the variable of interest may involve the destruction of the population unit;
• a population may be infinite.

Population parameter vs. sample statistic

Population parameter and sample statistic are two important concepts in statistics. Population parameter refers to a numerical value that describes a characteristic of an entire population, while sample statistic refers to a numerical value that describes a characteristic of a sample drawn from that population.

One goal of statistical inference is to estimate a population parameter from a sample statistic.

Parameters are

– Numerical characteristic of a population

– Constant (fixed) at any one moment

– Usually unknown

Statistics are

– Numerical summary of a sample

– Calculated from sample data (not constant)

– Used to estimate a parameter

Collecting data from a population

Collecting data from a population can be done in various ways depending on the research design and the population size. Here are a few common methods of collecting data from a population:

• Census: A census is a comprehensive study of the entire population, where data is collected from every member of the population. The census is generally conducted by the government and is used for administrative and planning purposes.
• Sampling: Sampling is a process of selecting a subset of individuals from the population to represent the entire population. The sample is usually selected randomly to minimize bias and increase the accuracy of the results. Sampling can be done through various methods like simple random sampling, stratified sampling, and cluster sampling.
• Surveys: Surveys are questionnaires or interviews that are conducted to collect data from individuals. Surveys can be conducted through various methods like face-to-face interviews, telephone interviews, or online surveys.
• Observations: Observations involve watching and recording the behavior of individuals or groups. Observations can be conducted in natural settings like schools, workplaces, and homes, or in a controlled laboratory setting.
• Experiments: Experiments involve manipulating one or more variables to observe their effect on the population. Experiments are generally conducted in a controlled laboratory setting, but can also be conducted in natural settings.

Collecting data from a sample

Collecting data from a sample is a common approach in research when it is not practical or feasible to study an entire population. A sample is a smaller subset of the population that is selected to represent the characteristics of the population. Here are a few common methods of collecting data from a sample:

• Simple random sampling: This is a method of selecting a sample where each member of the population has an equal chance of being selected. This can be done using a random number generator or by assigning numbers to each member of the population and selecting a subset of those numbers.
• Stratified sampling: This is a method of selecting a sample where the population is divided into subgroups based on certain characteristics and a sample is selected from each subgroup. This method ensures that the sample is representative of the population.
• Cluster sampling: This is a method of selecting a sample where the population is divided into clusters or groups, and a subset of clusters is selected. Then, a sample is taken from each selected cluster.
• Convenience sampling: This is a non-random method of selecting a sample where participants are selected based on their availability or willingness to participate. This method may introduce bias into the sample and is generally considered less reliable than other methods.

Sampling error

Sampling error is the difference between the characteristics of a sample and the characteristics of the population from which the sample was drawn. It occurs due to the random variability in selecting a sample from a population. In other words, the characteristics of a sample are likely to differ from the characteristics of the population due to chance, even if the sample was selected randomly.

Sampling error can have a significant impact on the accuracy of research findings. If the sample is not representative of the population, the conclusions drawn from the study may not be valid or generalizable to the larger population. Therefore, it is important to minimize sampling error by using appropriate sampling methods, ensuring an adequate sample size, and selecting a sample that is truly representative of the population.

The size of the sampling error is affected by several factors, including the size of the sample, the variability of the population, and the sampling method used. Larger samples tend to have smaller sampling errors, while more variable populations tend to have larger sampling errors. Sampling methods that are more representative of the population, such as stratified random sampling, tend to have smaller sampling errors than methods that are less representative, such as convenience sampling.

It is important to note that sampling error is just one type of error that can occur in research. Other types of errors include measurement error, bias, and confounding variables. However, minimizing sampling error is crucial for ensuring the reliability and validity of research findings.