Standard Deviation Formula: Definition and Example Problems
Standard Deviation Formula: Definition and Example Problems – What is meant by standard deviation and how to calculate it with the formula? On this occasion About the knowledge.co.id will discuss standard deviation along with formulas and examples of problems. Let's look at the discussion together in the article below to better understand it.
Standard Deviation Formula: Definition and Example Problems
In Statistics and Probability, Standard Deviation or also known as Standard Deviation is a statistical technique used to explain homogeneity within a group.
Standard deviation is also defined as a statistical value that is often used in determining how the data is distributed in the sample, as well as how close the individual data points are to the mean or average of the values of the sample Alone.
The word Standard Deviation was first introduced in 1894 by Karl Pearson in his book entitled On The Dissection Of Asymmetrical Frequency Curves.
Standard deviation is defined by the Square Root of Variance, because the number is a positive number and has the same units as a data set. There is one thing we need to know, before we discuss the standard deviation formula. The standard deviation value of the data set can be = 0 or it can even be greater or less than zero (0).
If the value is equal to zero, then all values in the set are equal.
Whereas a value whose value is greater or smaller indicates that the individual data point is far from its average value.
If we want to find the standard deviation value, the first step we need to do is as follows:
- First, calculate the average value of each existing data point.
The Average Value is equal to the sum of all the values in the data set
And we divide by the total number of points from the data. - Not only that, the next steps are: Then calculate the deviation for each data point from its average. Namely by subtracting the value from the average value.
- Next, we square the deviation of each data point and then find the average individual squared deviation.
- The resulting value is called the variant.
- After that, if you want to find the standard deviation, that is by taking the square root of the variant value.
Standard Deviation Formula
The following is the standard deviation formula, namely:
Population Standard Deviation
A population can be symbolized by σ (sigma) and can also be defined by a formula like the following:
Sample Standard Deviation
The standard deviation of the sample, the formula is as follows:
Counting
Determining the basis for calculating the variance is the desire to know the variation of each data group.
So that you can find out the variation of a data group, namely by reducing the data values along with the average of the data group. After that, all the results are added up.
It's just that this method can no longer be used because the result will always be 0 (zero).
So, so that the result does not become 0, then what we do is by squaring each reduction in data value and the average of the data group is then done by adding.
That way, the result of the sum of the squares will have a positive value.
Variant values that have been obtained from the division of the results of the sum of the squares with the data size (n).
However, when the variance value is applied, it is usually used to estimate the population variance. By using the formulas above, the value of the population variance will be greater than the sample variance.
In order not to be able to predict the population variance, n is used as a divisor for the sum of the squares and must be replaced with n-1 (degrees of freedom) so that the sample variance values approach the population variance.
So the sample variance formula will be like this:
The value of the variant that has been obtained is a squared value.
For example, the average value unit is grams (g) so the variant value is grams (g) squared.
In obtaining the unit value, the variance is squared again so that the result can be the standard deviation.
To simplify the calculation, the formula for the variance and standard deviation can be derived.
4. Variant Formula
The variant formula is as follows:
5. Standard Deviation Formula
The standard deviation formula is as follows:
Information :
s2 = variant
s = standard deviation
xi = i-th value of x
= Average
n = Sample size
Examples of Standard Deviation Problems
Problem 1.In a class that has a total of 40 students, then the class will be used as a sample to measure the height of 9 students, and the following data is obtained:
165, 170, 169, 168, 156, 160, 175, 162, 169.
Calculate the standard deviation of the sample data above.
So it is known that the Standard Deviation Value is 5.83.
Problem 2Mr. Ariyanto took the height of 10 students at SD Suka Jaya as a sample. Below is sample data collected by Mr. Ariyanto:
172, 167, 180, 170, 169, 160, 175, 165, 173, 170
Then, calculate the standard deviation based on the problem above.
Answer:
It is known that the amount of data (n) = 10 and (n-1) = 9. After that, you first look for the variant. To make it easier to calculate, you can also arrange a table like the image below.
From the table above, the next step is to calculate as below.
Then, plug it into the Variant formula. So it will be like this:
So from here we already know that the variance value is 30.32. Therefore, for how to calculate the standard deviation, you only need the square root value of the variance.
s = √30.32 = 5.51
So, the standard deviation of the example above is 5.51.
Thus the review from About the knowledge.co.id about Standard Deviation Formula, hopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
List of contents
Recommendation:
- √ Definition of Carving, Types, Techniques and Motives (Complete) Definition of Carving, Types, Techniques and Motives (Complete) - On this occasion we will discuss the Art of Carving. In this discussion, we explain the meaning of carving, types of carving, art techniques…
- Standard Deviation: Definition, Function, Formula, How to Calculate… Standard Deviation: Definition, Functions, Formulas, How to Calculate and Examples of Problems - Is it a standard deviations and examples?, On this occasion Se regarding the knowledge.co.id will discuss it and of course about other thing…
- √ Definition of Frequency Distribution, Type, Composition and… Definition of Frequency Distribution, Types, Arrangement and Parts - In this discussion we will explain about Frequency Distribution. Which includes the definition, types and arrangement of frequency distributions with complete and easy discussion...
- Papers: Definition, Characteristics, Functions, Types, Structures, Methods… Papers: Definition, Characteristics, Functions, Types, Structure, How to Make and Examples - What is meant by Papers and how to write them properly and correctly? On this occasion Seputarknowledge.co.id will…
- Short Story Text: Definition, Characteristics, Structure, Elements and Examples Short Story Text: Definition, Characteristics, Structure, Elements and Examples - What is a Short Story Text? Let us…
- √ 18 Definition of Risk According to Experts (Discussion of… 18 Definition of Risk According to Experts (Full Discussion) - In this discussion we will explain about risk. Which explanation is based on the statements of experts with their respective opinions.…
- Basic Volleyball Techniques: Definition and History Basic Volleyball Techniques: Definition of Volleyball and Its History - What are the basic techniques of playing volleyball? On this occasion, Seputarknowledge.co.id will discuss basic volleyball techniques and…
- Cartesian Coordinates: Definition, System, Diagram and Examples… Cartesian Coordinates: Definition, Systems, Diagrams and Example Problems - What do you mean by Cartesian coordinates ?On this occasion, Seputarknowledge.co.id will discuss Cartesian coordinates and other things covers it.…
- Definition of Data Communication and Components &… Definition of Data Communication and Its Components & Characteristics - On the last occasion we have discussing the meaning of data, this time a little different, here we will discuss what it is data communication,…
- √ Definition of Data and Information, Characteristics, Functions & Differences Definition of Data and Information, Characteristics, Functions & Differences - Data and information, many of us do not know about the difference between the two. Even more so many do not know the meaning or...
- Uniformly Changing Circular Motion: Definition, Magnitude… Uniformly Changing Circular Motion: Definition, Physical Quantity, Formulas and Examples of Problems - What is Motion Circular Changes Regularly and Examples? On this occasion, Seputarknowledge.co.id will discuss it and of course about...
- Definition of Data Analysis, Procedures and Types of Data Analysis Definition of Data Analysis, Procedures and Types of Data Analysis - In this discussion we will discuss data analysis. Of course, some people are still very new to the term data analysis.
- 12 Types and Definitions of Database According to Experts 12 Types and Understanding of Databases According to Experts - Here I will discuss what a database is and the types of databases. A database, also known as a database, is a…
- Faith in Qada and Qadar: Understanding, Proof, Wisdom and… Faith in Qada and Qadar: Definition, Proposition, Wisdom and Their Functions - What is meant by Faith in Qada and Qadar?
- Vector: Definition, Material, Formulas and Example Problems Vector: Definition, Material, Formulas and Example Problems - What is meant by Vector in operation mathematics? On this occasion, Around the Knowledge.co.id will discuss vectors and other matters about it.…
- Geometry Series: Definition, Formulas, Properties and Example Problems Geometry Series: Definition, Formulas, Properties and Example Problems - What is a geometric series?
- Environmental Speech: Definition, Purpose, Characteristics and… Environmental Speech: Definition, Purpose, Characteristics and Examples - How is the text of environmental speech structured? what's good and right?, On this occasion, Seputarknowledge.co.id will discuss it and of course things Which…
- √ 22 Definitions of Painting, Techniques, Elements, Tools, Materials,… 22 Definitions of Painting, Techniques, Elements, Tools, Materials, Flow & Examples - In this discussion, we will explain the art of painting. The discussion includes the definition of painting according to experts,…
- Definition of Learning Methods: Characteristics, Purpose, Types and… Definition of Learning Methods: Characteristics, Purpose, Types and Discussion - What is meant by Method Learning?, On this occasion, Seputarknowledge.co.id will discuss it and of course about other things Also…
- √ Gross Domestic Product: Definition, Types and Formulas Gross Domestic Product: Definition, Types and Formulas - On this occasion, Around Knowledge will discuss Gross Domestic Product. Which in this discussion explains the meaning of domestic product…
- √ 12 Definitions of Statistics, Purpose, Benefits, Functions &… 12 Definition of Statistics, Purpose, Benefits, Functions & Types (Complete) - In this discussion we will explain statistics. The discussion here includes the meaning of statistics according to experts, statistical purposes, statistical benefits,...
- Optical Instruments: Definition, Functions, Types and Parts Optical Instruments: Definition, Functions, Types and Parts - What are optical devices and what are their types? On this occasion, Seputarknowledge.co.id will discuss it and of course other things that...
- Rounders Game: Definition, History, Techniques, Infrastructure… Game Rounders: Definition, History, Techniques, Infrastructure and Value System - Do you know what it's called rounders game? Which…
- Craft Arts: Definition, History, Function, Purpose, Elements,… Craft Art: Definition, History, Function, Purpose, Elements, Types and Examples - What is meant by craft arts and their purpose? about…
- Microscope Images: Definition, History, Types, Parts, How to… Microscope Images: Definition, History, Types, Parts, How Microscopes Work and Care - How close are they do you recognize the shape and function of a microscope? At this time, about the knowledge Microscope…
- 74 Definition of Education According to Experts 74 Definition of Education According to Experts – Humans have been educated since they were born into the world until they enter school. The word education is no longer foreign to our ears, because all...
- Types of Color Types: Definition, Characters and Explanations Types of Color Types: Definition, Characters and Explanations - What are the types of colors and their explanations? On this occasion, Seputarknowledge.co.id will discuss it and of course the things that also cover it.…
- Microsoft Excel Is A Data Processing Application Program… Microsoft Excel is a very useful data processing application program. For some people, you must be familiar with Microsoft Excel, because you are used to using it. Microsoft Excel is an application program…
- Quartile Deviation Formula: Definition, Types and Example Problems Quartile Deviation Formula: Definition, Types and Example Problems - What is the quartile deviation and what's the formula? other…
- Sharia Accounting: Understanding According to Experts, Basic… Syari'ah Accounting: Understanding According to Experts, Legal Basis, Characteristics, Purpose, Principles, Characteristics And The advantages - What is sharia accounting and its advantages? discuss it and...