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Chetto983

Mathematical Calculator MCP Server

by Chetto983

confidence_interval

Compute the confidence interval for a dataset's mean to estimate the range likely containing the true population mean. Enter numerical values and an optional confidence level.

Instructions

Computes the confidence interval for the mean of a dataset.

Args: data: A list of numerical values. confidence: The confidence level (default is 0.95).

Returns: On success: {"confidence_interval": <(lower_bound, upper_bound)>} On error: {"error": }

Examples: >>> import numpy as np >>> np.random.seed(42) # For reproducible results >>> confidence_interval([1, 2, 3, 4]) # doctest: +ELLIPSIS {'confidence_interval': (0.445739743239..., 4.554260256760...)}

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
dataYes
confidenceNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv1.1.1

TDQS

B3.2/5.0
Behavior3/5

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

With no annotations, the description carries the full behavioral burden. It does disclose the success and error return shapes, which is valuable given there is no output schema, but it omits important behavior: distribution/t-distribution assumptions, behavior on empty or single-element data, and validation failures for out-of-range confidence values.

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?

Purpose is front-loaded, and the Args/Returns/Examples structure is scannable. The doctest example with numpy import, random seed, and an ELLIPSIS-pinned numeric output is longer than needed and adds little selection value.

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

Completeness4/5

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

For a simple two-parameter statistical function with no output schema, the description provides purpose, parameter meaning, and return shapes in both success and error cases. The main gaps are the assumed distribution and edge-case handling, which are secondary for this tool's complexity.

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?

Schema description coverage is 0%, so the description must compensate. It names both parameters and clarifies that 'confidence' is a confidence level (not a count), but largely restates type/default information already present in the schema and never states the valid range (e.g., 0 < confidence < 1).

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?

States a specific verb and resource: computing the confidence interval for the mean of a dataset. This is inherently distinguishable from statistical siblings like mean, variance, and standard_deviation, though the description never explicitly names an alternative or boundary case.

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?

No guidance on when to use this tool versus mean, variance, or standard_deviation. There is no mention of prerequisites (e.g., minimum sample size) or conditions under which a confidence interval is or isn't appropriate.

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