Population vs Sample in Statistic

Last Updated : 22 Feb, 2024

In statistics, understanding the difference between a population and a sample is fundamental to many aspects of data analysis and inference.

Population Vs Sample

The population refers to the entire group of individuals or items that we are interested in studying and drawing conclusions about. In statistics, the population is the entire set of items from which data is drawn in the statistical study. It can be a group of individuals or a set of items.

The population is usually denoted by N.

A sample is a subset of the population selected for study. It is a representative portion of the population from which we collect data in order to make inferences or draw conclusions about the entire population.

It is denoted by n.

Population

Sample

The population includes all members of a specified group.

A sample is a subset of the population.

Collecting data from an entire population can be time-consuming, expensive, and sometimes impractical or impossible.

Samples offer a more feasible approach to studying populations, allowing researchers to draw conclusions based on smaller, manageable datasets

Includes all residents in the city.

Consists of 1000 households, a subset of the entire population.

Collecting Data From Population and Sample

Populations are used when your research question requires, or when you have access to, data from every member of the population. Usually, it is only straightforward to collect data from a whole population when it is small, accessible and cooperative.

Example:

A marketing manager for a small local bakery wants to understand customer preferences for different types of bread sold at their shop. Since they are solely interested in analyzing the preferences of customers who visit their bakery, they decide to collect data on bread preferences from every customer who makes a purchase over the course of a month. By using the entire dataset of bread purchases, including preferences indicated by customers, they aim to identify trends and patterns in bread choices specifically among their bakery’s clientele.

When your population is large in size, geographically dispersed, or difficult to contact, itâ€™s necessary to use a sample. With statistical analysis, you can use sample data to make estimates or test hypotheses about population data.

Example:

Suppose you are conducting research on smartphone usage habits among teenagers in a specific city. Your population comprises all teenagers aged 13-18 living in that city, which could number in the tens of thousands. Due to logistical constraints and the difficulty of reaching every teenager in the city, you opt to use a sample of 500 teenagers randomly selected from different schools within the city. This sample will participate in interviews or surveys to provide insights into their smartphone usage patterns, preferences, and behaviors.

When Should Samples be used?

• When studying a large population where it is impractical or impossible to collect data from every individual.
• When resources such as time, cost, and manpower are limited, making it more feasible to collect data from a subset of the population.
• When conducting research or experiments where it is important to minimize potential biases in data collection.

Population And Sample Formulas

Population Parameters:

Mean: The population mean is defined by [Tex]\mu[/Tex]. And it’s formula is given by,

[Tex]\mu = \frac 1 N \Sigma X[/Tex] , N= Number of elements in population.

Standard Deviation: The population standard deviation is given by [Tex]\sigma[/Tex]. And it’s formula is given by:

[Tex]\sigma = \sqrt {\frac 1 N {\Sigma(X-\mu)^2}}[/Tex]

Sample Statistic:

Mean: The Sample mean is given by [Tex]\bar x[/Tex]. And its formula is given by,

[Tex]\bar x = \frac 1 n \Sigma x[/Tex]

Standard Deviation: The sample standard deviation is given by s. And it’s formula is given by,

[Tex]s= \sqrt {\frac 1 {n-1} {\Sigma(x-\bar x)^2}}[/Tex]

Sample Statistic

It is a numerical characteristic that describes the entire population

Statistics are calculated from sample data and serve as estimates or approximations of the corresponding population parameters

Parameters are typically unknown and must be estimated.

Calculated using data from a sample drawn from the population. Statistics are directly computed from sample data.

Calculated using data from a sample drawn from the population. Statistics are directly computed from sample data.

Used to estimate population parameters based on sample data. Statistics help researchers infer population characteristics from a representative subset of the population

Example:

When examining the height of adult males in a country, the population parameter represents the population mean height (Î¼), which reflects the average height of all adult males nationwide. However, due to the impracticality of measuring the length of each individual, this parameter remains unknown and must be estimated. In contrast, a sample statistic such as the sample mean (xÌ„) is derived from a subset of the population, in this case a random sample of 500 male adults from different regions of the country. By measuring the heights of these individuals and averaging them, researchers obtain a sample statistic that serves as an approximate population parameter. This process makes it possible to draw conclusions about the height distribution of adult men in the country, based on the characteristics observed in the sample.

1. What is a population parameter?

A population parameter is a numerical characteristic of a population. Examples include the population mean, population variance, population standard deviation.

2. What is a sample statistic?

A sample statistic is a numerical characteristic of a sample. It’s used to estimate the corresponding population parameter. Examples include the sample mean, sample variance, sample standard deviation, etc.

3. What is sampling error?

Sampling error is the difference between a sample statistic and the corresponding population parameter. It occurs due to randomness in the selection of the sample.

4. What is sampling bias?

Sampling bias occurs when a sample is not representative of the population. It can lead to inaccurate conclusions about the population.

5. What are some common methods of sampling?

Common sampling methods include simple random sampling, stratified sampling, cluster sampling, systematic sampling, and convenience sampling.

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