3-Statistics: Population and Sample

Population and Sample: Understanding Statistical Inference

In the below picture-1, there is a gathering of millions of people.

Table of Contents.

If we want to take the opinion of all these people about the opinion about voting in an election for A, B & C Political parties. We will face the below problems.
It will require an infrastructure to take the opinion
Financially it will be very costly
It will be very time-consuming to contact each & every person
Practically it does not seem feasible.

How to overcome the practical constraints and get meaningful information?

Solution:-

In place of contact with each & every person, we will select a small group of persons. Refer to the yellow rectangles in the below photograph.

Talk to these selected groups of people only (inside the Yellow rectangle) for conducting an opinion poll.

Conduct an opinion poll of people in the selected groups (Yellow rectangles).

Compile opinion poll data and derive voting patterns (an example).

Sample opinion:-

- - - Party A – 48% voting
    - Party B – 27% voting
    - Party C – 19% voting
    - Do not know – 6%

Now we will assume that a whole gathering of millions of people (Picture-1) have the same opinion as the Sample opinion.

Population opinion: –

- - - Party A – 48% voting
    - Party B – 27% voting
    - Party C – 19% voting
    - Do not know – 6%

Statistics: Population definition

Population is the set of all individuals of interest in a particular study.
As mentioned in Case Study (A), the gathering of people may be treated as POPULATION in statistics terminology.

Example 2: In the below word map children’s populations on Earth are shown as a red dot. All the children will be treated as a Population under statistical study.

In most cases, the Population is very large in number. Therefore it becomes practically impossible to evaluate every child of the population. (Due to financial, resource & time constraints, etc)
Therefore samples are selected for the study. Sample statistical analysis helps to predict population behavior.

Statistics: Sample definition

A sample is a subgroup of the population.
A group of individuals selected from a population is called a sample.
In Example 2 :
- One vaccine has been developed for children. Now we are going for the trial of this vaccine on children. We cannot do a trial on the entire children population. Therefore we will select children for trial. In the below figure, green circles represent children selected as samples for a vaccine trial.

The sampling method is economical and less time-consuming.
A sample is intended to be representative of its population.
The outcome from samples is considered as an outcome of the population.
However, there is a certain amount of error when inference is drawn from the sample. This error is known as sampling error.

Statistics Sampling error

Sampling error is the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter
A sampling error is a statistical error that occurs when an analyst does not select a sample that represents the entire population of data. As a result, the results found in the sample do not represent the results that would be obtained from the entire population.

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