Statistics in your search for a certain data group that shares a characteristic, makes a great focus on everyday items that are useful for an investigation. However, when we speak of trend, it refers to a high number of individuals that is governed by something, but when we refer to central tendency, it is represented as a midpoint to which a distribution leans.

Advantages and disadvantages of statistics

When it comes to statistics we can say that there are 3 great advantages over it:

  • Statistics allow a systematic working method to be carried out.
  • Unfounded ideas are not the basis for this branch and avoid by all means making claims without any basis.
  • The claims that are argued are guided to achieve improvements that are based on evidence with objective data.

As for disadvantages, we can say that they only exist when there is a misuse of statistics, which produces:

  • Erroneous data based on missing numbers.
  • If the study is not adequate, negative decisions can be made that do not help to improve the processes.
  • You need enough time, dedication, and calculation to deliver accurate results.

What do measures of central tendency represent and what are their advantages?

When we talk about Measures of Central Tendency, we mean intermediate data between a set of values, helping us to summarize everything in a single number. They collaborate to obtain the similarities in the statistical sets, and to group them with certain patterns and certain similarities in order to calculate trends between these data sets, and thus find similarities around a central value.

It is because of them that I allows to visualize the similarity of data groups to each other in order to describe them in some way. Comparing or interpreting the results obtained to establish and set a limit and values ​​towards which the variable being evaluated tends to be located. In turn, there are three types of central measurements, the arithmetic mean, the median and the mode, and depending on the evaluation you are going to make, you can use one of them.

Among its advantages are:

  • Focus a large study on a single issue.
  • It helps to group similar sets which makes the calculation easier and more orderly.
  • It allows making comparisons from different points of view.

Average, properties, advantages and disadvantages

Many times the Arithmetic Mean is defined as an average value of each data in some set. We speak of the total sum of all observations that are divided by the total number of observations. It should be noted that it has a single value in which different data intervene to determine it. It is representative when the data are homogeneously distributed.

An example of this can be the academic bulletin whose average is obtained based on the sum of all the subjects seen in a year, the result of which is divided among themselves.

Advantage

  • It is easy to calculate the reason why it is the most used trend measure.
  • It is stable with a large number of observations.
  • When making your calculation, makes use of all possible data.
  • It is very useful in statistical procedures.
  • It is susceptible to any change in the data, functioning in this way as a data variation detector.

Disadvantages

  • It is usually sensitive to values ​​that are too high or too low.
  • It is impossible to perform qualitative calculations or data that have open-ended classes, either lower or higher.
  • We must avoid using it in distributions that are asymmetric.

Characteristics, advantages and disadvantages of Fashion

The value it has is determined by its frequency, making it not a unique value, making it exist two or more values ​​that have the same frequency. As it is a quantitative variable, it is represented. It is usually represented a large number of times in a data set. In short, it is the observation that is repeated the most.

Advantage

  • Does not require calculations.
  • It can be used in qualitative as well as quantitative calculations.
  • It is not at all influenced by some extreme value.
  • Can be very useful when we have different values ​​in groups.
  • They can be calculated in open-ended classes.

Disadvantages

  • It is difficult to interpret data if you have more than three modes, or more.
  • If we have a reduced data set, its value is useless.
  • If there is data that is repeated, it usually does not exist.
  • Does not use all available data information.
  • It is generally too far from the middle of the data obtained.

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Properties, advantages of using the Median and its disadvantages

When we find data positioned from lowest to highest, we know that it is the central value. It should be noted that its value is unique and merely depends on the order of the data. It is more representative than the mean when there are very high or very low numerical values ​​in the sample, depending relatively on the statistical situation.

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Advantage

  • It is easy to calculate if the number of data is not that large.
  • Its influence by extreme values ​​is null, since it is only influenced by the central values.
  • It can be applied to perform a calculation of quantitative data, up to data with an open extreme class.
  • Supports ordinal scale. Turning it into the most representative measure of central tendency in all kinds of variables.

Disadvantages

  • No use is made of all the information we have when making your calculation.
  • To use it we must order all the information first.
  • It does not weight the values ​​before determining it.
  • Extreme values ​​are likely to be important

Properties, advantages and disadvantages of the arithmetic mean

The arithmetic mean is known as that total amount of the variable that is distributed in equal parts between each observer. It is also known as half and it is a practical way to summarize the information of a distribution, assuming that the group of observers handle the same quantity of variable.

Now, among its properties we have to:

  • It does not have an eigenvalue of the variable. That is, if the arithmetic mean of a group of school subjects is 9, it may be that in fact none of the subjects had a specific grade of 9. The arithmetic mean is an element highly sensitive to changes and values ​​in the data. .
  • The arithmetic mean behaves very similar to common mathematical operations such as addition

When talking about advantages It can be said that the arithmetic mean is the most widely used and that is why almost everyone knows it and makes its calculation practical and easy to handle. On the other hand, this measure makes it possible to detect variations in the data.

As for its disadvantages, it must be it is very sensitive to variations and this makes the data of the statistical distribution not so accurate.

measures of central tendencies

Properties, advantages and disadvantages of the harmonic mean

The harmonic mean is the reciprocal of the arithmetic mean, that is, it is the result of a number of elements between the sum of the inverses of each of these figures.

Among its properties are:

  • Its inverse is the arithmetic mean of the inverses of the figures of the variables.
  • It is less than or equal to the arithmetic mean in all cases.
  • If properly transformed, the data can go from a harmonic mean to an arithmetic mean.

Among its advantages is that all the values ​​of the distribution are within the calculation and it is usually a little more representative than the arithmetic mean, in some cases.

Among its disadvantages is the fact that it cannot be calculated in distributions whose value is equal to 0. On the other hand, it has to be highly influenced by small values ​​and due to this it does not have to be used in this type of calculation.

Properties, advantages and disadvantages of the geometric mean

The geometric mean is frequently used in calculations of average percentage growth rates for some series. This is defined as the root of the product of a set of positive numbers. All the values ​​of a set are multiplied by each other and if, for example, one of them is 0, the final result would be 0.

Within its properties you have to:

  • The logarithm within the geometric mean is equal to the arithmetic mean of the logarithms of the values ​​of a variable.
  • In a set of positive numbers, the geometric mean is always less than or equal to the arithmetic mean.

When talking about its advantages we have that the geometric mean takes into account each of the values ​​of a distribution and becomes less sensitive than the arithmetic mean in terms of extreme values.

Among its disadvantages we can find that its statistical significance becomes less intuitive compared to the arithmetic mean and, at the same time, its calculation is a bit more difficult to perform. On the other hand, if any of its values ​​is equal to zero, the arithmetic mean is not determined since it is canceled.

The main thing is that these measures belong to measures of central tendency, so their numerical values ​​tend to locate the central part of a data set. Added to this you have to:

  • There is a positive asymmetry between them when the mean is greater than the median and is called Distribution skewed to the right.
  • There is also a negative skewness that occurs when the mean is less than the median and is called Left skewed distribution.

When the distribution becomes symmetric, the mean, the mode, and the median coincide in their value.