standard_deviation

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

With no annotations, the description carries the full behavioral burden and does fairly well: it documents the return shape ({"result": ...}) and the error shape ({"error": ...}). The worked example with [1, 2, 3, 4] -> 1.118... implicitly disambiguates the crucial sample-vs-population convention (this is sample stdev, ddof=1). It stops short of stating edge-case behavior for empty or single-element lists.

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?

Front-loaded summary sentence followed by compact Args/Returns/Examples sections; the structure is skimmable and each section adds information. Slightly heavier than necessary for a one-parameter function but nothing is wasted.

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?

No output schema exists, so the Returns block and example are doing necessary work and are present. For a simple unary math function the description is nearly self-sufficient; only the sample-vs-population convention (implied, not stated) and edge-case handling remain implicit.

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%, so the description must compensate, and it does: "data: A list of numerical values" clarifies the element type and constraint that the bare schema (array of number, title "Data") does not spell out. One parameter, adequately described.

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+resource ("Computes the standard deviation of a list of numbers"), matching the tool name exactly and making the operation unambiguous. However, it never differentiates itself from close siblings such as variance or mean, which an agent could plausibly confuse for this statistical operation.

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?

No when-to-use guidance is given: nothing explains when to pick standard_deviation over variance, mean, or median, nor any preconditions on the input. Usage is only inferable from the mathematical name itself.

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