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PRACTICE 3: DATA DESCRIPTION AND SIMPLE ANALYTICAL METHODS

PLAN:

1. The concept of the variational series.

2. Ordering the variational series.

3. Ranking, median, and mode.

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The word "Variation" originates from the Latin word "variatio", which signifies change, difference, or fluctuation.

A variational series refers to a sequence that demonstrates the relationship between observed values and their repetition (frequency). Essentially, it is an arrangement of data points that pairs each unique value with the number of times it occurs.

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The method of ordering a variational series involves systematically determining the repetition frequency of random numbers.

For example, a psychologist administered the Heka and Hesse neurosis detection methodology to 25 adolescents. The obtained raw scores can be arranged in the following statistical series:

6, 7, 10, 12, 20, 5, 7, 13, 10, 6, 10, 8, 13, 7, 9, 12, 11, 12, 8, 9, 10, 12, 11, 8, 9.

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It is also possible to add or accumulate the frequencies of a variational series. The accumulated frequencies represent the total sum of values in a sequence, starting from the first frequency up to the last. This accumulation of frequencies is known as frequency cumulation.

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Ranking is a method used in the ordinal scale. In this scale, categories (groups) of objects are ordered. Therefore, the values of the traits cannot be changed arbitrarily—the hierarchy of the objects must be preserved.

Example: Class students can be ranked from highest to lowest or lowest to highest based on the scores they received from a specific assessment.

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We will rank the results of Fetiskin’s "Verbal Diagnostics of Personality Self-Esteem" methodology applied to 9 students:

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The lowest ranks are assigned to the highest scores. This situation can also be reversed.

If the obtained results are identical, the ranking is performed as follows:

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The Median is defined as the variant that divides an ordered variational series into two equal parts and is denoted by “Md”. The method for determining the median depends on whether the number of variants is even or odd. Since the following series 1, 9, 6, 8, 12, 3 is even, there are two middle values here: 6 and 8. There is a specific method for calculating the median when there are two middle numbers:

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If the number of items in a series is odd, the median is found as follows:

In the series 5, 6, 2, 9, 10, 12, 18, 8, 7, the median is located exactly in the middle of the numbers that are smaller and larger than it. That is: 8

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The Mode refers to the most frequently occurring value in a data set. It is denoted by the symbol “M”

2 4 7 8 9 4 6 4 6

In this case, 4 is the mode, because it is repeated 3 times in the series.