# THE RELATIVE DISPERSION AND FRACTILES

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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.

Contents

### 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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