THE RELATIVE DISPERSION AND FRACTILES

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In this article, we’ll be talking about relative dispersion and fractiles. Grab your pen and paper.

Comparing degrees of variability based on the absolute values could be misleading since some measures of absolute dispersion, for example, a variance is only significant in relation to the mean used in its calculation.

It, therefore, becomes necessary to express an absolute measure of dispersion relative value.

A most commonly used measure of relative dispersion is the coefficient of variation, V, given by;

V = S//X × 100

Example
The average mark scored by a student in a term is 64.1 with a standard deviation of 6.1.

The same student reads on an average of 5.3 hours daily with a standard deviation of 2.1 hours.

Which distribution is the subject is to a greater dispersion?

Solution:
The coefficient of variation for the marks is:
V = S//X × 100 = 6.1/64.1 × 100 = 9.5%

The coefficient of variation for reading  is:
V = S//X × 100 = 2.1/5.3 × 100 = 39.6%

Therefore, the hours-spent on reading has a greater dispersion.

Fractiles (Measures of Partition)

There are basically three measures of partition namely; Quartic, Deciles, and percentiles.

  1. Quartiles
    Theses are three points that divide a distribution into four equal parts. They are denoted by Q12 Q22 and Q32
    1. The lower first quartile: Q1 is the value below which twenty-five (25%) of the data can be found.
    2.  The second quartile: Qis the value below and above which fifty percent (50%) of the data lie. It is equal to the median.
    3. The upper or the third quartile: Q3 is the value above which twenty-five percent of the data can be found.
  2.  Deciles
    These are the nine points that divide a distribution into ten equal parts. The nine points of the deciles are denoted by D1 D2… D
  3. Percentiles
    These are 99 points that divide the entire distribution into one hundred equal parts. The points are denoted by D1 D2… D

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