Arithmetic average

What is the arithmetic mean?

The arithmetic mean, also known as average, is the value obtained by add all the data and divide by the total amount of data.

One of the fundamental problems confronting a statistical analysis consists of searching for a representative value of a series of values; In other words, if you have a quantity that varies, either in space or time, you will need to obtain its predominant level.

The value provided by this predominant grade or level is the half.

When the arithmetic mean is calculated, the variation is neglected and only the predominant value, which is a great advantage in the statistical summary.

The value of the arithmetic mean depends on each of the measurements that make up the series and is affected by extreme deviations from the average.

Uses of the arithmetic mean

The uses of the arithmetic mean are as follows:

• The arithmetic mean is the most used average because it can be calculated for any kind of progression, logically preferably in those that follow an arithmetic progression.
• It is applicable in those series where, by existing zero or negative terms, some averages cannot be calculated. So also in homogeneous series or when there are large variations between the terms that form them.
• The arithmetic average is also used in the case of proportional variations.

How to calculate the arithmetic mean?

The value of the arithmetic mean is obtained by sum all data what do you have and divide the result by the total number of that data.

The arithmetic averages are divided into simple Y weighted:

• Simple: one that attributes the same importance to the different terms of the series or, expressed in technical terms, the same weight, the same weighting.
• Weighted: that in which each term of the series of values ​​is influenced by a quantitative factor that totally modifies it; As indicated, this quantitative factor is called the weight or weight.

The arithmetic average symbol is

and the simple arithmetic mean is calculated as follows:

Given the above, the calculation of the arithmetic mean for the values ​​4, 6, 8, 10, 16, 28 would be as follows:

Regarding the weighted arithmetic mean, if there is a series of values ​​X₁, X₂, X₃,… Xn, their respective weights being P₁, P₂, P₃,… Pn, the weighted arithmetic mean will be given by the following formula:

Based on the above and in accordance with the following data, if different units of a certain item have been sold at different prices, as shown below ...

• 16 units at US $ 8.
• 20 units at US $ 5.
• 18 units at US $ 7.

… The calculation of the weighted average price of the item sold would be:

Examples of arithmetic mean

Simple arithmetic mean

Below are the ages of the 22 players of the Brazilian football team, who participated in the 1970 Mexico Soccer World Championship:

Player	Age
Felix	32
Ado	25
Leao	twenty
Brito	30
Wilson piazza	27
Charles Albert	25
Marco Antonio	19
Baldochi	24
Fontana	29
Everaldo	25
Joel camargo	2. 3
Ze Maria	twenty-one
Clodoaldo	twenty
Gerson	29
Tostão	2. 3
Rivelino	24
Paulo caesar	twenty-one
Jairzinho	25
Pele	29
Robert	25
Edu	twenty
Darius	24

The total sum of the ages is 540. To determine the ages of each of the members of the champion team, the completed years of the players were taken at the time of the Mexico 70 World Cup staging.

With an average age of 24-55 years, the Brazilian team that dazzled soccer fans at the 1970 World Cup in Mexico has been, so far, the youngest team in history to achieve this crown.

Weighted arithmetic mean

In the company Example, CA, the payroll of 100 workers has the following salary distribution:

No. of workers	Monthly salary in US $
40	800
25	1,000
twenty	1,250
fifteen	1,500

The above information would be arranged as follows:

X	Wages		800	1,000	1,250	1,500
P	Weighing		40	25	twenty	fifteen

And in order to determine the weighted arithmetic mean, the information would be completed as follows:

X	800	1,000	1,250	1,500	Total
P	40	25	twenty	fifteen
X * P	32,000	25,000	25,000	22,500	104,500

According to this, the result of the weighted arithmetic average would be:

Bibliography:

How is the arithmetic mean calculated? Recovered from yosoytuprofe. García, Israel and García Juan Antonio. The arithmetic mean. Teacher Training and Research in Mathematics Education, vol.6, 197-217. University of La Laguna. Santa Cruz de Tenerife - Spain. 2004. González, Ernesto. General Statistics (6th ed.). Editions of the Library of the Central University of Venezuela. Caracas Venezuela. 1979.