standard_deviation

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

With no annotations provided, the description carries the full behavioral burden. It discloses the sample standard deviation formula, the ValueError for fewer than 2 numbers, the dictionary return type, and that the operation is logged. This is solid behavioral context for a simple calculator tool.

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 well-structured with a clear opening sentence followed by Args, Returns, Raises, and Notes sections. It is appropriately sized for the tool's complexity, front-loads the main purpose, and contains no filler.

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 math operation, the description covers purpose, input shape, sample versus population behavior, error conditions, return type, and logging. Given the low complexity and the existence of an output schema, nothing critical 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%, so the description must compensate for the parameter. It explains that data is a ListOperation object containing a list of numbers and adds the key semantic constraint that fewer than 2 numbers raises ValueError, which the schema does not express.

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 begins with a specific verb and resource: 'Calculate the standard deviation of a list of numbers.' This clearly identifies the operation and distinguishes it from sibling statistics tools like mean and median, as well as arithmetic operations.

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 usage context is implied rather than explicit: an agent can infer it is for measuring variation via standard deviation. The note about using sample standard deviation (n-1 denominator) provides some selection guidance, but it does not explicitly contrast with alternatives or state when not to use this tool.

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