Population and Sample in Statistics

In statistics, population and sample is an important topic. It is very helpful in statistics for the collection of data. In statistics, the set of data is collected and selected from a statistical population with the help of some procedures. Basically, there are two different types of data sets which are population and sample. When we do the calculation of standard deviation, mean deviation, and variance it is important to know whether we are referring to the entire population or only the sample. If the population size is denoted by n then the sample size of that population is given by n-1.


Population

Population includes all the elements of the data set and measurable terms of the population like mean, and standard deviation which is known as parameters.

Population refers to the entire group of people, objects, events, etc.

There are different types of populations that we will discuss in detail.

  1. Finite population

  2. Infinite population

  3. Existent population

  4. Hypothetical population.

Now a detailed explanation about population and sample is given below.


Sample

The sample is part of the population. The sample includes one or two observations that are extracted from the population. 

The characteristic that can be measured, of the sample, is called a statistic. The process of selecting samples from the population is known as sampling.

For example, some students in the class are the sample of the population.

The sampling process is divided into two types they are,

  1. Probability sampling,

  2. Nonprobability sampling.

We will discuss both the types in detail and will try to understand them.


Probability sampling

Probability sampling is based on the fact that every member of the population has equal chances of being selected.

In probability sampling, the population unit cannot be selected at the discretion of the researcher.

This method is also known as random sampling.

There are some techniques which are used in probability sampling they are given below,

  • Simple random sampling.

  • Multi-stage sampling.

  • Cluster sampling.

  • Stratified sampling.

  • Optimum allocation stratified sampling.

  • Proportionate sampling.

  • Disproportionate sampling.


Population and Sample Examples

  1. All the students in the school are the population and the students of class 10 are the sample.

  2. Patients in the hospital are the population and the old age patients are the sample.


Population and Sample Formula

We will discuss some formulas for mean absolute deviation, variance, and standard deviation based on the population and the given sample.

Let n be the population size and n-1 be the sample size than the formula for MAD,  variance, and standard deviation are given by,

Population MAD = \[\frac{1}{n}\sum |x_{i}-x^{-}|\]

Sample MAD =\[\frac{1}{n-1}\sum |x_{i}-x^{-}|\]

Population variance = \[\frac{1}{n}(x_{i}-x^{-})^{2}\]

Sample variance = \[\frac{1}{n}(x_{i}-x^{-})^{2}\]

Population standard deviation = \[\sqrt{\frac{1}{n}\sum (x-x^{-})^{2}}\]

Sample standard deviation = \[\sqrt{\frac{1}{n-1}\sum (x-x^{-})^{2}}\]

FAQ (Frequently Asked Questions)

1.Explain Non Probability Sampling

Answer : Non Probability sampling is the method of sampling where the samples are collected in the process where not all individuals get an equal chance of being selected.

In non-probability sampling, the population units can be selected at the discretion of the researcher.

These samples will be using human judgments for selecting units and not a theoretical basis.

There are different techniques for non-probability sampling which are given below,

  • Quota sampling.

  • Judgment sampling.

  • Purposive sampling.

2. Elaborate Types of Population. 

Answer: There are four types of populations. 

Finite Population

The population which is finite and can be counted is known as finite population.  It is also known as a countable population.

Infinite Population

The infinite population is defined as the population which is infinite and cannot be counted. It is also known as an uncountable population.

Existence Population

The existing population is defined as a population of concrete individuals. In other words, the population whose unit is out there in solid form is understood as an existent population. 

Hypothetical Population

The population during which whose unit isn't available in solid form is understood as the hypothetical population. A population basically consists of sets of observations, objects, etc. that are all something in common. In some situations, the populations are only hypothetical.