The average value in the statistics is... Average values


2018-10-13 11:00:33




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Everyone in the modern world, planning to take out a loan or making stock of vegetables for the winter, periodically faced with a term such as “average”. Let's find out: what it is, what its types and classes exist, and why it is used in statistics and other disciplines.

Average value - what is it?

A Similar name (SV) is a generalized aggregation of homogeneous phenomena to be determined in any one quantitative variable basis. averages

However, people who are far from so abstruse definitions to understand this concept, as the average number of something. For example, before you take out a loan, the Bank employee will ask a potential client to provide information on the average income for the year, which is the total amount earned by human resources. It is calculated by summing earned for the whole year and dividing by the number of months. Thus, the Bank will be able to determine whether his client to pay the debt in time.

Why is it used?

As a rule, the average values are widely used in order to give a summary description of certain social phenomena of massive proportion. They can also be used for smaller calculations, as in the case of a loan, in the example above. the average value of the trait

However, most averages still apply for global purposes. As an example, one of the examples is the calculation of the quantity consumed by the citizens of electricity for one calendar month. Based on the data in the future, sets maximum standards for categories of the population receiving benefits from the state.


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Also, using average values is developed a guarantee the service life of certain household appliances, cars, buildings, etc. based On the collected data in this way was once developed by contemporary norms of work and rest.

In fact, any phenomenon of modern life, wearing a massive scale, one way or another necessarily connected to the concept.


This phenomenon is widely used in almost all the exact Sciences, particularly those of an experimental nature.

Find the average value of the magnitude has enormous significance in medicine, engineering disciplines, cooking, Economics, politics, etc.

Based on data obtained from similar generalizations, and develop therapeutic drugs, training program, establish the minimum subsistence level wages, build schedules, produce furniture, clothes and shoes, hygiene items and more.

In mathematics this term is called the “average” and is used for the implementation of the various examples and tasks. Most of them are simple addition and subtraction of ordinary fractions. As is known, to solve these examples, you must bring both fractions to a common denominator.

Also in the Queen of the exact Sciences is often applied is close in meaning to the term “the average value of a random variable". The majority of it is more familiar as the "expectation", usually considered in the theory of probability. It is worth noting that a similar phenomenon is also applied when making statistical calculations.

The Average value in the statistics

However, often study the concept is used in statistics. As you know, the science itself specializiruetsya on the calculation and analysis of the quantitative characteristics of mass social phenomena. Therefore, the average value in the statistics used as a specialized method of achieving its main task - the collection and analysis of information. average

The Essence of this statistical method is to replace individual values of the considered characteristic the particular balanced average.

As example is the famous joke about the food. So some factory on Tuesdays at lunch his boss usually eats shepherd's pie, a simple workers – braised cabbage. Based on these data it can be concluded that the average plant staff on Tuesdays dinner cabbage rolls.

Although this example is slightly exaggerated, but it illustrates the main drawback of the method find the average of values – the leveling of the individual features of objects or persons.

In statistics, data averages are used not only for analysis of the collected information but also for planning and forecasting future actions.

Also it helps to assess the results achieved (e.g., implementation of the plan for the cultivation and harvest of wheat for the spring-summer season).

How to calculate

Although depending on the view of ST. there are different formulas for its calculation, in the General theory of statistics, usually used only one method of calculating the average value of the characteristic. To do this, first add together the values of all phenomena, and then divide the resulting amount by the number of them. average magnitudeWhen making such calculations, it is worth remembering that the average value always has the same dimension (or units) that separate unittogether. RMS value

Terms of the correct calculations

Discussed above the formula is quite simple and universal, so wrong it is almost impossible. However, it is necessary to consider two aspects, otherwise the data obtained will not reflect the real situation.

  • Specifying the individual values (on the basis of which the average is calculated) should always refer to homogeneous populations, and their number must be considerable.

    In the above joke meat casserole and cabbage – belong to one category – “food”. However, if one were to know how many pounds of cabbage is stored in the dining room of the plant, consider the data about the meat, it would not make sense, as in this case, they did not refer to considering homogeneous populations. the average value in statistics

  • In any individual case, it is important to take into account the qualitative content of the sign, the average value you want to calculate. It is important to pay attention to the relationship between the studied characteristics and the available data for calculations.

Classes SV

Finding answers to basic questions: "the Average value - what is it?", "Where it is used?" and "How can I calculate it?", you should know what classes and types of SV exist.

First of all, this phenomenon is divided into 2 classes. This is a structural and exponential averages.

Types power SV

Each of these classes, in turn divided into species. Have the power of a class four. the mean of a random variable

  • The arithmetic Average value – this is the most common form of SV. It represents a secondary component, in the determination of which the total volume of the considered characteristic in the data set equally distributed between all units of a given population.

    This form is divided into categories: simple and weighted arithmetic SV.

  • The Average harmonic magnitude – indicator, reverse simple arithmetic average, computed from the inverse values of the considered trait.

    It is used in cases when you know the individual values of the trait and the work, and the data frequency - no.

  • The median value is most often applicable in the analysis of growth phenomena. It enables to keep unchanged the product of the individual values of this quantity, not amount.

    Also happens to be easy and balanced.

  • Root mean square value used in the calculation of the individual indicator metrics, such as coefficient of variation, characterizing the rhythm of production, etc.

    Also, it calculates the average diameters of the pipes, wheels, middle side of the square, and similar shapes.

    Like all other kinds of middle SV, the standard is simple and balanced.

Types of structural variables

In Addition to medium-ne, statistics are often used structural types. They are better suited to calculate the relative characteristics of the varying values of the symptom and the internal structure of the ranks of the distribution.

These types of there are two.

  • Fashion. This type is most often used to determine the most popular among buyers of clothing sizes and footwear.

    usually, the fashion is calculated according to this formula. the average value is
    it M0 – is the value fashion, x0 – the lower boundary of the modal interval, h & ndash; the size of the considered interval, fM – its frequency fM-1 – frequency preceding the modal interval and fM+1 – frequency.

  • The Median is called the characteristic value of the underlying ranked number and dividing it into two parts, equal among themselves on the numerical indicator.

    In formulae, this species is designated as ME.

    depending on which number is determined by the form of the structural SV (discrete or interval of variation), apply various formulas of its calculation.

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