Statistics in its search for a certain set of data that share a characteristic makes a great focus on everyday elements that are useful for an investigation. However, when we talk about tendency, 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 is inclined.
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 work method to be carried out.
- Unfounded ideas are not a basis for this branch and avoid making unfounded claims at all costs.
- The assertions 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:
- Wrong data based on unverified numbers.
- If the study is not adequate, negative decisions can be made that do not help to improve the processes.
- It needs enough time, dedication and calculation to offer exact 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 due to them that it is possible to visualize the similarity of the data groups with each other in order to describe them in some way. Comparing or interpreting the results obtained to establish and fix a limit and values ​​towards which the variable being evaluated tends to be located. In turn, there are three types of central measures, the arithmetic mean, the median and the mode, and depending on the evaluation you are going to do, you can use one of them.
Among its advantages are:
- Focus an extensive study on a single number.
- It helps to group similar sets which makes the calculation easier and more orderly.
- It allows comparisons from different points of view.
Media, properties, advantages and disadvantages
The Arithmetic Mean is often defined as an average value of each data in some set. We speak of the sum total of all observations 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 is 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, whose result is divided among themselves.
Advantage
- It is easy to calculate, which is why it is the most used trend measure.
- It is stable with a large number of observations.
- When making 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 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, whether they are lower or higher.
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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 two or more values ​​exist that have the same frequency. Being a quantitative variable, it is represented. It is usually represented a large number of times in a data set. In short, it is the most repeated observation.
Advantage
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It does not require calculations.
- It can be used in qualitative and quantitative calculations.
- It is not influenced at all by any extreme value.
- It can be very useful when we have different values ​​in groupings.
- 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.
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It does not use all 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 ranked from smallest to largest, 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
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It is easy to calculate if the number of data is not so 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, even data with extreme open class.
- Supports ordinal scaling. Making it the most representative measure of central tendency in all kinds of variables.
Disadvantages
- Not all of the information we have is used in making your calculation.
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To use it we must sort all the information first.
- It does not do a weighting of 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 ¨Mean¨ and it is a practical way to summarize the information of a distribution, assuming that the group of observers handle the same amount of variable.
Now, among its properties you 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 actually be that in none of the subjects a 9 has been given as a specific grade. The arithmetic mean is a highly sensitive element to changes and values ​​in the data. .
- The arithmetic mean behaves much like common mathematical operations like 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 something practical and easy to handle. On the other hand, this measure allows detecting variations in the data.
As for its disadvantages, it is very sensitive to variations and this means that the data of the statistical distribution are not as accurate.
Properties, advantages and disadvantages of the Harmonic Mean
The harmonic mean is reciprocal to the arithmetic mean, that is, it is the result of a number of elements divided by the sum of the inverses of each of those figures.
Among its properties you have to:
- Its inverse is the arithmetic mean of the inverses of the numbers of the variables.
- It is less than or equal to the arithmetic mean in all cases.
- If the data is properly transformed, it 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 on distributions whose value is equal to 0 . On the other hand, it is very influenced by small values ​​and due to this it does not have to be used in this type of calculations.
Properties, advantages and disadvantages of the geometric mean
The geometric mean is frequently used in calculations of average percentage growth rates of 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 together 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 consideration 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 cancels.
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. In addition to this, you have to:
- Between them there is a positive asymmetry 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 the Left Skewed Distribution.
When the distribution becomes symmetric, the mean, mode, and median are the same in value.
