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In the field of statistics, a parameter is a number that summarizes a characteristic of an entire population.
A population includes all members or elements of a defined group that we are interested in studying.
Because the population is the whole set, the parameters remain consistent and assume the value of the entire population. When we talk about parameters, think of data like the average (mean), proportion, or total that represents every single individual in that group.
For example:

• The average age of all students at a certain college.
• The total income of all households in a city.
• The exact percentage of people voting for a specific candidate in an election.

These values won't change unless there is a change in the entire population.
Parameters give us precise insights into the population, but often populations are too large to measure directly.
In these cases, we often rely on sampling and statistics to make reasonable estimates of these parameters.

A statistic is a value that summarizes a characteristic of a sample, which is a subset of the population.
Unlike parameters, statistics can vary depending on which individuals are included in the sample. Because samples are used to draw conclusions about the larger population, statistics help us make educated guesses about parameters.
Think of statistics as the tools that provide smaller snapshots of a larger picture. For example:

• The average height of students in three randomly selected classrooms within a school.
• The proportion of a sample of voters supporting a new policy.
• The average income of residents within a sample of 100 households of a city.

One crucial aspect of statistics is their variability.
Different samples from the same population may produce different statistics due to the natural variation between samples.
Thus, the selection of the sample is crucial in accurately estimating the true population parameter.

Grasping the distinction between a population and a sample is fundamental in statistics.
A **population** includes everyone and everything we wish to understand or measure.
This could be the set of all students in a university, every citizen in a country, or all the fish in a lake. A **sample**, on the other hand, is a smaller group or subset selected from the population.
Samples are used because it's often impractical or impossible to measure an entire population.
By studying a sample, researchers aim to infer conclusions about the overall population. Key differences include:

• Size: Populations are typically large, whereas samples are smaller and more manageable.
• Variability: Samples must accurately represent the population, so they are selected to reduce bias.
• Purpose: We use populations for complete analysis but rely on samples for estimations due to feasibility.

Understanding these terms helps in choosing the right techniques for data collection and analysis.
Proper sampling ensures accurate results and meaningful conclusions about the population.