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apetta

Vibe Math MCP

by apetta

Statistical Analysis

statistics
Read-onlyIdempotent

Compute descriptive statistics, quartiles, and IQR-based outlier detection for numerical data. Obtain count, mean, standard deviation, min, max, median, Q1, Q2, Q3, IQR, and outlier values. Select analysis types as needed.

Instructions

Comprehensive statistical analysis using Polars.

Analysis types: - describe: Count, mean, std, min, max, median - quartiles: Q1, Q2, Q3, IQR - outliers: IQR-based detection (values beyond Q1-1.5×IQR or Q3+1.5×IQR)

Examples:

DESCRIPTIVE STATISTICS: data=[1,2,3,4,5,100], analyses=["describe"] Result: {count:6, mean:19.17, std:39.25, min:1, max:100, median:3.5}

QUARTILES: data=[1,2,3,4,5], analyses=["quartiles"] Result: {Q1:2, Q2:3, Q3:4, IQR:2}

OUTLIER DETECTION: data=[1,2,3,4,5,100], analyses=["outliers"] Result: {outlier_values:[100], outlier_count:1, lower_bound:-1, upper_bound:8.5}

FULL ANALYSIS: data=[1,2,3,4,5,100], analyses=["describe","quartiles","outliers"] Result: All three analyses combined

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
contextNoOptional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
output_modeNoOutput format: full (default), compact, minimal, value, or final. See batch_execute tool for details.full
dataYesList of numerical values (e.g., [1,2,3,4,5,100])
analysesYesTypes of analysis to perform

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes
Behavior4/5

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

Annotations already indicate readOnly and idempotent behavior. The description adds transparency by detailing the computation types and output structures through examples, clarifying that no side effects occur.

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 well-structured with a clear header, bulleted analysis types, and separate examples. It is appropriately detailed without being overly verbose, though some repetition could be trimmed.

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

Completeness5/5

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

Given the tool's moderate complexity and the presence of an output schema, the description thoroughly explains input parameters, analysis types, and output formats through examples. No critical gaps remain.

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

Parameters4/5

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

Schema coverage is 100%, but the description adds value by explaining the purpose of each analysis type and providing concrete examples that illustrate parameter usage (data, analyses, context).

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

Purpose5/5

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

The description clearly states the tool performs 'Comprehensive statistical analysis using Polars' and lists specific analysis types (describe, quartiles, outliers) with detailed examples. This distinguishes it from sibling tools like array_statistics or correlation, which are more specific.

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

Usage Guidelines3/5

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

The description implies usage for basic statistical summaries but does not explicitly state when to use this tool versus alternatives like correlation or array_statistics. No guidance on prerequisites or exclusions is provided.

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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