What are the Advantages and Disadvantages of Core Trend Measures?

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 talk about 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.

What are measures of central tendency?

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 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 measures , the arithmetic mean, the median and the mode .

What are the advantages and disadvantages of the arithmetic mean?

Many times the Arithmetic Mean is defined as an average value of each data in some set. 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.

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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 .

What are the advantages and disadvantages of the Median?

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
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What are the 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.

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.

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