Statistics in its search for a certain group of data that share a characteristic, **makes a great focus on everyday elements 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.

Index( )

__Advantages and disadvantages of statistics____What do measures of central tendency represent and what are their advantages?____Average, properties, advantages and disadvantages____Characteristics, advantages and disadvantages of Fashion____Properties, advantages of using the Median and its disadvantages____Properties, advantages and disadvantages of the arithmetic mean____Properties, advantages and disadvantages of the harmonic mean____Properties, advantages and disadvantages of the geometric mean__

__Relationship between Mean, Mode and Median__

**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 refer to **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 it is **allowed to visualize the similarity of the 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 **unique 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 carrying out its calculation, it
**makes use of all possible data**. - It is very useful in statistical procedures.
- It is susceptible to any change in the data, thus
**functioning as a detector of variations in data**.

**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 single value, making there are **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**

**It 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.
- It 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 the 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.
**It does not use all the available data information**.- It is usually too far from the middle of the data obtained.

**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.

**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. Making it 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 equally** among each observer. It is also known as *¨Media¨* and it is a practical way of summarizing the information of a distribution, assuming that the group of observers handle the same amount 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 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.

**Regarding its disadvantages, it** is very sensitive to variations and this makes the data of the statistical distribution not so accurate.

**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 is 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 is less sensitive than the arithmetic mean in terms of extreme values.

**Among its disadvantages we can find** that its statistical meaning is less intuitive compared to the arithmetic mean and, at the same time, its calculation is a little 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.

**Relationship between Mean, Mode and Median**

The main thing is that these measures belong to the 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 skewness between them when the mean is greater than the median and is called
*a right-skewed distribution.* - There is also a negative skewness that occurs when the mean is less than the median and is called
*a Left-skewed distribution.*

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