Population and Sample: Overview, Questions, Preparation

Statistics, in the simplest form, can be defined as a way to study data. It starts with a collection of data that is analysed, interpreted, organised, and then presented in a specific form. Population and sample are amongst the most important elements of statistics that have been simplified for a better understanding and application. 

Population

It is a collection of all the data that is directly related to the area of study. The data set is inclusive of some measurable characteristics that are called parameters. Parameters are mean and variance deviation. The simplest example: all people living within a region will be considered its population. The population is further classified into the following:

Finite population: An easily countable group of individuals is a finite population. 

Infinite population: A larger group of individuals that can’t be counted or is uncountable is referred to as an infinite population. 

Existent population: Concrete individuals or objects are collectively called an existent population; for example, books, coins, students, etc.

Hypothetical population: As the term suggests, it is a larger group that is nearly impossible to count. 

Sample

It is a set of smaller groups that are selected from the larger set for analysis. In statistics, there can be one or more sample groups to analyse. The process of observing and withdrawing measurable results from the sample is referred to as statistics. A sample involves:

Probability sampling

Here the researcher chooses the sample group out of the larger group to study. The selection process is based on the below-mentioned techniques:

1. Simple random sampling
2. Cluster sampling
3. Stratified sampling
4. Disproportionate sampling
5. Proportionate sampling
6. Optimum allocation stratified sampling
7. Multi-stage sampling

Non-probability sampling

Here all the members of the population do not have an equal chance to be in a sample. The selection techniques used are:

1. Quota sampling
2. Judgment sampling
3. Purposive sampling

Population and Sample Formulas

It is an integral part of the maths syllabus of Class 11 and for various engineering exams such as JEE. You may have explored the idea of chance in earlier classes to measure the uncertainty of different phenomena. It has a weightage of almost 15% of the final exams’ marks. 

1 What does 0.05 mean in statistics?

Solution.

P > 0.05 is the probability that the null hypothesis is true. 1 minus the P-value is the probability that the alternative hypothesis is true. A statistically significant test result (P ≤ 0.05) means that the test hypothesis is false or should be rejected.

2.What does the P-value of 1 mean?

Solution.

When the data is perfectly described by the restricted model, the probability to get data that is less well described is 1. For instance, if the sample means in two groups are identical, the p-values of a t-test are 1.

3. What is the p-value for a 95 confidence interval?

Solution.

A quick way to remember the relationship between the 95% confidence interval and p-value of 0.05 is to consider the confidence interval as arms that ‘embrace’ values that are consistent with the data.

Q: What are the examples of population and sample?

Q: What are the factors contributing to sample size collection?

Q: What factors influence the sample size?

Q: Why is it easier to use a sample than to use a population?

Q: Define the sampling population.