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

No annotations are provided, so the description carries the full burden; it does disclose two real behavioral facts (z defaults to 1.96, sample SD uses n-1) beyond the bare purpose. However it says nothing about edge cases like n<2, invalid input handling, or what the result looks like, which is a meaningful gap for a zero-annotation 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?

Purpose and formula are front-loaded in one dense sentence, with zero filler. The trailing emoji trial-promo tag is the only noise and slightly dilutes an otherwise tight definition.

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?

Given no annotations, no output schema, and 0% schema coverage, the definition is only adequate: it conveys the computation and defaults but omits input string formatting, return shape, and failure behavior an agent would need to call it correctly.

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 coverage is 0%, so the description must compensate and it partially does: it explains z as a critical value defaulting to 1.96 and values as the value series. But it never clarifies the input encoding for these string-typed params (comma-separated list? JSON array?), leaving the actual call format ambiguous.

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 names a specific verb+resource ("Computes the margin of error") and even supplies the exact formula z * sampleSD / sqrt(n), which lets an agent distinguish it from statistical siblings like x402-standard-error or x402-confidence-interval-mean. It stops short of explicitly naming those alternatives, so a 4 rather than a 5.

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?

There is no when-to-use or when-not-to-use guidance and no reference to sibling tools, despite a crowded family of statistics helpers. The formula implies a statistical context but gives no exclusions or routing hints.

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