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IBM

MCP Math Server

by IBM

harmonic_mean

Calculate the harmonic mean of positive numbers to find the average of rates or ratios, useful for comparing data with different units or scales.

Instructions

Calculate harmonic mean of a list of positive numbers. (Domain: arithmetic, Category: harmonic_series)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
numbersYes
Behavior2/5

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 states the tool calculates harmonic mean for 'positive numbers', which is a constraint not in the schema. However, it lacks details on behavior such as error handling for non-positive inputs, return format, or performance characteristics. More behavioral context would be helpful given the absence of annotations.

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

Conciseness5/5

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

The description is extremely concise and front-loaded: a single sentence that directly states the tool's purpose and constraints, followed by domain/category tags. There is no wasted verbiage, making it efficient for quick understanding.

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

Completeness3/5

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

Given the tool's low complexity (single parameter, no output schema, no annotations), the description is somewhat complete but has gaps. It covers the basic purpose and a key constraint (positive numbers), but lacks details on return values, error cases, and usage compared to siblings. For a simple arithmetic tool, it's minimally adequate but could be more informative.

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

Parameters3/5

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

The input schema has 0% description coverage, but the description adds some semantic context: it clarifies that 'numbers' should be 'positive'. This compensates partially for the schema gap. However, it does not explain the array structure, expected length, or numeric types beyond positivity, leaving some ambiguity.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Calculate harmonic mean of a list of positive numbers.' It specifies the verb ('calculate'), resource ('harmonic mean'), and domain/category context. However, it does not explicitly differentiate from sibling tools like 'mean' or 'harmonic_number', which could provide similar statistical calculations.

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

Usage Guidelines2/5

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

The description provides minimal usage guidance. It mentions the domain ('arithmetic') and category ('harmonic_series'), but does not specify when to use this tool versus alternatives like 'mean' or 'harmonic_number' (which are siblings). No explicit when-to-use or when-not-to-use instructions are given.

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

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