position measurements

position measurements

1. Position measures divide a data set into groups with the same number of individuals. To calculate position measures it is necessary that the data are ordered from smallest to largest. In statistics, there are two types of measures of position: measures of central position, which allow determining the central values ​​of a data set, and measures of non-central position, which are used to divide the data into equal intervals.

2. FEATURES They must be rigorously defined and not be susceptible to various interpretations. They must depend on all the observations in the series, otherwise it would not be a characteristic of the distribution. They should not be too abstract in nature. They must be capable of algebraic calculation, fast and easy.

3. parameters

   • The position parameters have the function of locating the distribution along the values ​​of it. Depending on the existence or not of phenomena such as asymmetry, anomalous data, coexistence of subpopulations, etc., different parameters may be more useful. The main position parameters are:

4. classification

   • Non-central position measurements Position measures are usually divided into two large groups: non-central trend and central. The non-central measures of position are the quantiles. These perform a series of equal divisions on the ordered distribution of the data. In this way, they reflect the top, middle and bottom values. The most common are:
     • The quartile: It is one of the most used and divides the distribution into four equal parts. Thus, there are three quartiles. The lower values ​​of the distribution are located below the first (Q1). The middle or median are the lower values ​​equal to quartile two (Q2) and the higher ones are represented by quartile three (Q3).
     • The quintile: In this case, it divides the distribution into five parts. Therefore, there are four quintiles. Furthermore, there is no value that divides the distribution into two equal parts. It is less frequent than the previous one.
     • The decile: We are facing a quantile that divides the data into ten equal parts. There are nine deciles, from D1 to D9. The D5 corresponds to the median. On the other hand, the upper and lower values ​​(equivalent to the different quartiles) are located at intermediate points between them.
     • The percentile: Finally, this quantile divides the distribution into one hundred parts. There are 99 percentiles. It has, in turn, an equivalence with deciles and quartiles.
   • Center position measurements These allow us to summarize the distribution of the data in a single central value, around which they are located; while the latter divide the distribution equally. These have already been developed in other Economipedia articles, therefore, we will limit ourselves to offering brief information on each one.
     • The arithmetic, geometric or harmonic mean: These are three central measures that indicate a weighted average of the data. The first is the most used and the best known of the three. The geometric is applied in series that show percentage growth. For its part, the harmonica is useful in the analysis of investments in the stock market.
     • The median: In this case, this is the most recognizable measure of central position. Divide the distribution into two equal parts. In this way, it expresses the median value, not the mean. It is very useful in variables such as income or salaries, while it is closely related to the mean and some of the quantiles seen.
     • The mode: This is a central measure of the most frequent values. Therefore, fashion informs us about those that are repeated on more occasions. This measure is very useful in market research when we measure an impression on a product with a likert scale.

5. Importance of Statistical Position Measures They are the first step that must be taken in the descriptive analysis. When we want to know information about a phenomenon, we start by collecting data. But these, by themselves, are not going to provide us with relevant information, which is why they must be analyzed. The position measurements, together with the dispersion measurements, help us to group them and even to codify them. These are the main and basic knowledge in statistics. In fact, introductory college classes focus on them. If we do not know what an average is, it is more than likely that we do not know how to understand other concepts such as regression or hypothesis testing. For this reason, it is one of the essential knowledge in sciences such as economics.

6. USES/APPLICATIONS They are indicators used to indicate what percentage of data within a frequency distribution exceeds these expressions, whose value represents the value of the data found in the center of the frequency distribution. Position measurements try to find measurements that synthesize frequency distributions.

   • ADVANTAGE They provide information about the data series we are analyzing. The frequency distribution is located. It is easily obtainable.
   • DISADVANTAGES It is sensitive to extreme values. The influence of small values.

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