descriptive_statistics

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations present, the description carries the full burden and does disclose meaningful edge-case behavior: at least one value is required, and sample stdev/variance require two values and are ``null`` otherwise. This is exactly the kind of behavioral detail an agent needs to avoid misinterpreting output, though it says nothing about error behavior if the constraint is violated.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three short sentences, front-loaded with the purpose, then the output inventory, then the edge-case constraint. No filler and no repetition of the schema.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a single-parameter pure function with an output schema already defining the return shape, the description covers purpose, returned fields, and the input edge cases completely. Nothing an agent needs to invoke or interpret it correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, but there is only one parameter (``numbers``) whose name and type make its meaning self-evident, and the description adds a genuine constraint beyond the schema: a minimum length of one, and two for the sample-based statistics. That is real added meaning over a bare array-of-numbers schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ("Return summary statistics for a list of numbers") and enumerates the exact statistics produced (count, sum, min, max, mean, median, population/sample stdev, variance). This clearly distinguishes it from every sibling, which are symbolic/algebraic tools (differentiate, integrate, matrix_multiply) rather than summary-statistics tools.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is implied — the description makes clear it is the tool to reach for when you have a raw list of numbers and want aggregate statistics — but it never states when to use it versus alternatives or any preconditions beyond the input cardinality. No explicit when-not guidance is given.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.