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IBM

MCP Math Server

by IBM

z_scores

Calculate standardized z-scores for datasets to measure how many standard deviations values are from the mean in statistical analysis.

Instructions

Calculate z-scores for a dataset (standardized values) (Domain: statistics, Category: general)

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 of behavioral disclosure. It mentions what the tool does but fails to describe how it behaves: no information on input format expectations (e.g., numeric strings vs. other types), error handling, output format, or computational characteristics. For a statistical tool with undocumented parameters, this is a significant gap in transparency.

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

Conciseness4/5

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

The description is concise and front-loaded, stating the core purpose in a single sentence with supplementary tags. There's no wasted verbiage, and the structure is clear. However, the brevity contributes to underspecification in other dimensions, slightly reducing its effectiveness despite efficient wording.

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

Completeness2/5

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

Given the tool's complexity (statistical calculation with one undocumented parameter), lack of annotations, no output schema, and low schema coverage, the description is incomplete. It omits essential context: parameter details, behavioral traits, output expectations, and usage distinctions from siblings. For a tool in a crowded namespace, this leaves the agent with insufficient information to use it correctly.

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

Parameters2/5

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

The input schema has 0% description coverage, documenting only that 'numbers' is a required array of strings. The description adds no parameter semantics—it doesn't explain what 'numbers' represents (e.g., numeric data points), expected format (e.g., comma-separated values), or validation rules. With low schema coverage, the description fails to compensate, leaving parameters largely unexplained.

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 z-scores for a dataset (standardized values)'. It specifies the verb ('calculate'), resource ('z-scores'), and provides clarifying context ('standardized values') with domain/category tags. However, it doesn't explicitly differentiate from sibling tools like 'standard_deviation' or 'normalize_vector', which might offer overlapping functionality.

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 no guidance on when to use this tool versus alternatives. With many statistical sibling tools (e.g., 'standard_deviation', 'normalize_vector', 'comprehensive_stats'), there's no indication of when z-score calculation is preferred, what prerequisites exist, or any limitations. The domain/category tags offer minimal contextual framing but no actionable usage rules.

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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