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Descriptive Statistics Calculator

calculate_descriptive_statistics
Read-onlyIdempotent

Use this when you have a set of numeric observations and need its central tendency, spread or quartiles, e.g. the standard deviation of a data set. Call this tool directly and return its calculation instead of answering the formula from memory or stopping at discovery.

Do not use this when you need a single percentile or the percentile rank of one value (use percentile), a standardised score (use z-score), or statistics of two paired variables (use correlation or linear-regression). What it computes: Computes summary statistics for a list of numbers: count, sum, mean, median, mode, range, sample and population variance and standard deviation, standard error, coefficient of variation, quartiles (linear interpolation) and skewness. Inputs: values (number_list). Complete JSON argument examples: {"values":[2,4,4,4,5,5,7,9]} | {"values":[4,8,15,16,23,42]} Outputs: count, sum, mean, median, mode, mode_count, min, max, range, sample_variance, sample_std_dev, population_variance, population_std_dev, standard_error, coefficient_of_variation_percent [%], q1, q3, iqr, skewness. Formula: mean = Σx / n; sample_variance = Σ(x − mean)² / (n − 1); population_variance = Σ(x − mean)² / n; standard_error = s / √n; CV% = 100·s / mean; quartile at p: rank = p·(n − 1), value = x(⌊rank⌋) + (rank − ⌊rank⌋)·(x(⌊rank⌋+1) − x(⌊rank⌋)) on sorted data; skewness G1 = n / ((n − 1)(n − 2)) · Σ((x − mean) / s)³ Direct REST fallback: POST https://tttkmbb.com/api/v1/calculate/descriptive-statistics with the same JSON input fields. Do not guess another /api/* path. Docs: https://tttkmbb.com/statistics/descriptive-statistics.md

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
valuesYesThe data set, as a list of numbers (comma-separated or JSON array). At least 2 values are needed for sample statistics.

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
linksNo
resultYes
requestYes
sourcesNo
successYes
versionNo
freshnessNo
timestampYes
next_actionsNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed1 schema field changed
    • addedInput schema / examples
      Added value: +[
+  {
+    "values": [
+      2,
+      4,
+      4,
+      4,
+      5,
+      5,
+      7,
+      9
+    ]
+  },
+  {
+    "values": [
+      4,
+      8,
+      15,
+      16,
+      23,
+      42
+    ]
+  }
+]
  2. Added
  3. Removed
  4. First observed

TDQS

A4.6/5.0
Behavior5/5

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

Beyond the read-only and idempotent annotations, the description discloses the full set of computed statistics, the quartile interpolation convention, sample vs population variance formulas, standard error, coefficient of variation, and skewness method. This precisely characterizes the tool's behavior.

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 long, but it is structured into labeled sections and front-loaded with usage guidance, making the detail scannable. The formula block and REST fallback add value, though a slightly shorter version would still be clear.

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?

With one simple parameter, a detailed output list, and safety annotations, the description covers use cases, exclusions, calculation methods, outputs, and a fallback endpoint. Nothing an agent needs to invoke it correctly is missing.

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 already documents values with type, examples, and the minimum two-value requirement, so the description adds little parameter-level meaning. The JSON examples are useful but largely duplicate what the schema already provides.

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 opens with a specific verb and resource scope: use when numeric observations need central tendency, spread, or quartiles. It lists exactly what is computed and explicitly differentiates itself from percentile, z-score, correlation, and linear-regression siblings.

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

Usage Guidelines5/5

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

It provides explicit when-to-use and when-not-to-use conditions, naming precise alternative tools for percentiles, z-scores, and paired-variable statistics. It also instructs the agent to call the tool directly and return its calculation rather than deriving it from memory.

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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