# Sample vs. Population

• /
• Blog
• /
• Sample vs. Population

## Population

A population is the entire group of individuals or objects that we are interested in studying. For example, the population could be all the people living in a certain city, all the students in a school, or all the cars on a certain road.

## Sample

A sample is a subset of a population. It is a smaller group of individuals or objects selected from a larger population. The sample represents the population, and we use statistics to make inferences or predictions about the population based on the sample. ## Statistic (NOT Statistics)

A statistic is a measure that describes a characteristic of a sample. For example, a sample's mean, median, mode, and standard deviation are all statistic. It is used to summarize and describe the sample data.

The sample mean is represented by x-bar, and it is calculated by summing all the values in the sample and dividing by the number of values in the sample. For example, if the values in the sample are 2, 3, 4, 5, and 6, then the sample mean would be:

$$\Large{\overline{x} = \frac{2 + 3 + 4 + 5 + 6}{5} = 4}$$

The sample standard deviation is represented by "s", and it is calculated by taking the square root of the sum of the squared differences between each value in the sample and the sample mean, divided by the number of values in the sample minus one. For example, if the sample mean is 4, and the values in the sample are 2, 3, 4, 5, and 6, then the sample standard deviation would be:

$$\Large{s = \sqrt{\frac{(2 - 4)^2 + (3 - 4)^2 + (4 - 4)^2 + (5 - 4)^2 + (6 - 4)^2}{(5 - 1)}} = 1.58}$$

## Parameter

A parameter is a measure that describes a characteristic of a population. For example, the population mean, median, and standard deviation are all parameters. Parameters are used to describe the population.

The population mean is represented by mu, and it is calculated by summing all the values in the population and dividing by the number of values in the population. For example, if the values in the population are 2, 3, 4, 5, and 6, then the population mean would be:

$$\Large{\mu = \frac{(2 + 3 + 4 + 5 + 6)}{5} = 4}$$

The population standard deviation is represented by $$\sigma$$, and it is calculated by taking the square root of the sum of the squared differences between each value in the population and the population mean divided by the number of values in the population. For example, if the population mean is 4, and the values in the population are 2, 3, 4, 5, and 6, then the population standard deviation would be:

$$\Large{\sigma = \sqrt{\frac{(2 - 4)^2 + (3 - 4)^2 + (4 - 4)^2 + (5 - 4)^2 + (6 - 4)^2}{5}} = 1.414}$$

 (adsbygoogle = window.adsbygoogle || []).push({}); 
###### About the Author Quality Gurus

Customers served! 1

Quality Management Course

FREE! Subscribe to get 52 weekly lessons. Every week you get an email that explains a quality concept, provides you with the study resources, test quizzes, tips and special discounts on our other e-learning courses.

 (adsbygoogle = window.adsbygoogle || []).push({}); 

Similar Posts:

December 26, 2022

## F Distribution

F Distribution

November 28, 2021

## 8 Elements of the Six Sigma Project Charter

8 Elements of the Six Sigma Project Charter

December 26, 2021

## Seven Quality Tools – Control Charts

Seven Quality Tools – Control Charts

November 30, 2021

## Visual Factory

Visual Factory

December 18, 2022

## Calculating Standard Deviation and Variance: Sample vs. Population

Calculating Standard Deviation and Variance: Sample vs. Population

December 22, 2022

## Union and Intersection in Probability

Union and Intersection in Probability

November 25, 2021

## The Complete Guide to SMART Goals and How they are the Key to Achieving Success

The Complete Guide to SMART Goals and How they are the Key to Achieving Success

October 31, 2021

## QG Certificate for Udemy Students

QG Certificate for Udemy Students

December 24, 2021

## Seven Quality Tools – Scatter Diagram

Seven Quality Tools – Scatter Diagram

32 Courses on SALE!