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

The annotations already declare readOnlyHint, idempotentHint, and openWorldHint, so the safety profile is covered. The description adds meaningful output-related context: it returns both sample and population standard deviations, variance, mean, and a deviation-by-deviation table, which is useful beyond the structured annotations.

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?

The description is short and front-loads the sample-vs-population distinction. The first sentence prompts the key parameter choice, and the second sentence lists the outputs. The URL and 'you can check' phrase are mildly extraneous but not disruptive.

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 simple two-parameter calculator with no output schema, the description adequately explains the return values (both standard deviations, variance, mean, deviation table). Annotations already cover safety and idempotency, so no further behavioral disclosure is needed.

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 100%, so the schema documents both parameters. The description still adds value by clarifying the difference between sample (n−1) and population (N) types, which goes beyond the schema's truncated 'Data is a…' description.

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?

The description clearly states that the tool returns both sample and population standard deviations, variance, and mean, with a deviation table. It names the specific resource (standard deviation) and distinguishes the two calculation modes, which is enough to separate it from sibling calculators like average_calculator.

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?

The description gives no guidance on when to use this tool versus alternatives such as average_calculator or z_score_calculator. It only asks whether the user wants sample or population, which is a parameter choice, not tool-selection guidance.

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