In statistics as well as in quantitative methodology, the set of data are collected and selected from a statistical population with the help of some defined procedures. There are two different types of data sets namely, population and sample. So basically when we calculate the mean deviation, variance and standard deviation, it is necessary for us to know if we are referring to the entire population or to only sample data. Suppose the size of the population is denoted by ‘n’ then the sample size of that population is denoted by n -1. Let us take a look of population data sets and sample data sets in detail.
Population
It includes all the elements from the data set and measurable characteristics of the population such as mean and standard deviation are known as a parameter. For example, All people living in India indicates the population of India.
There are different types of population. They are:
- Finite Population
- Infinite Population
- Existent Population
- Hypothetical Population
Let us discuss all the types one by one.
Finite Population
The finite population is also known as a countable population in which the population can be counted. In other words, it is defined as the population of all the individuals or objects that are finite. For statistical analysis, the finite population is more advantageous than the infinite population. Examples of finite populations are employees of a company, potential consumer in a market.
Infinite Population
The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. Example of an infinite population is the number of germs in the patient’s body is uncountable.
Existent Population
The existing population is defined as the population of concrete individuals. In other words, the population whose unit is available in solid form is known as existent population. Examples are books, students etc.
Hypothetical Population
The population in which whose unit is not available in solid form is known as the hypothetical population. A population consists of sets of observations, objects etc that are all something in common. In some situations, the populations are only hypothetical. Examples are an outcome of rolling the dice, the outcome of tossing a coin.
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Sample
It includes one or more observations that are drawn from the population and the measurable characteristic of a sample is a statistic. Sampling is the process of selecting the sample from the population. For example, some people living in India is the sample of the population.
Basically, there are two types of sampling. They are:
- Probability sampling
- Non-probability sampling
Probability Sampling
In probability sampling, the population units cannot be selected at the discretion of the researcher. This can be dealt with following certain procedures which will ensure that every unit of the population consists of one fixed probability being included in the sample. Such a method is also called random sampling. Some of the techniques used for probability sampling are:
- Simple random sampling
- Cluster sampling
- Stratified Sampling
- Disproportionate sampling
- Proportionate sampling
- Optimum allocation stratified sampling
- Multi-stage sampling
Non Probability Sampling
In non-probability sampling, the population units can be selected at the discretion of the researcher. Those samples will use the human judgements for selecting units and has no theoretical basis for estimating the characteristics of the population. Some of the techniques used for non-probability sampling are
- Quota sampling
- Judgement sampling
- Purposive sampling
Population and Sample Examples
- All the people who have the ID proofs is the population and a group of people who only have voter id with them is the sample.
- All the students in the class are population whereas the top 10 students in the class are the sample.
- All the members of the parliament is population and the female candidates present there is the sample.
Population and Sample Formulas
We will demonstrate here the formulas for mean absolute deviation (MAD), variance and standard deviation based on population and given sample. Suppose n denotes the size of the population and n-1 denotes the sample size, then the formulas for mean absolute deviation, variance and standard deviation are given by;
\(\begin{array}{l} \text { Population } \mathrm{MAD}=\frac{1}{n} \sum_{\mathrm{i}=1}^{n}\left|x_{i}-\bar{x}\right| \quad \text { Population Variance }=(\sigma x)^{2}=\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2} \\ \text { Sample } \mathrm{MAD}=\frac{1}{n-1} \sum_{i=1}^{n}\left|x_{i}-\bar{x}\right| \quad \text { Sample Variance }=(S x)^{2}=\frac{1}{n-1} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2} \\ \text { Population Standard Deviation }=\sigma x=\sqrt{\frac{1}{n} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}} \\ \text { Sample Standard Deviation }=S x=\sqrt{\frac{1}{n-1} \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}} \end{array}\)Difference between Population and Sample
Some of the key differences between population and sample are clearly given below:
Comparison | Population | Sample |
Meaning | Collection of all the units or elements that possess common characteristics | A subgroup of the members of the population |
Includes | Each and every element of a group | Only includes a handful of units of population |
Characteristics | Parameter | Statistic |
Data Collection | Complete enumeration or census | Sampling or sample survey |
Focus on | Identification of the characteristics | Making inferences about the population |
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What is the word that defines the results of the population that is not the average population? For example, you have the average height of a group of males as 6’8 but when you look closer, the group of males are all professional basket ball players so it’s not really an average of all males.
It would be – Population standard deviation.
Because standard deviation gives the measure for a group that actually spread out from the average(mean).
In case, if it is from Sample then the term used is – Sample Standard Deviation.