On which of the following options does the numerical taxonomy of plants is based?

The correct option is All observable characteristics.

Step-by-Step Explanation:

1. Definition of Numerical Taxonomy:
Numerical taxonomy (often associated with phenetics) is a classification system in biological systematics that groups organisms based on their overall similarity. It relies on the statistical and mathematical evaluation of a wide range of traits rather than relying on a few selected evolutionary markers.

2. Core Principles:
- Equal Weighting: Every observable character is given equal weight and importance in the analysis.
- Data Quantification: All observable physical and biological characteristics are converted into numerical data (such as presence/absence, or measured values).
- Use of Computers: Computers are utilized to process and analyze the vast numbers of characters and organisms simultaneously, calculating similarity coefficients to cluster related plants together.

3. Why other options are incorrect:
- Chemical constituents: Using chemical compounds (like alkaloids, carotenoids, and proteins) for classification is known as Chemotaxonomy.
- Chromosome number and Structure: Using cytological details of cells (such as chromosome number, structure, and behavior during cell division) for classification is known as Cytotaxonomy.

Thus, numerical taxonomy is uniquely characterized by its utilization of all observable characteristics to determine classification relationships.