OnlineCyberTools MCP (280+ filterable tools)

math_statistics_calculator

Read-onlyIdempotent

Compute descriptive statistics, z-scores, Pearson/Spearman correlation, or simple linear regression for numeric datasets. Choose from four modes to analyze single or paired data.

Instructions

Statistics Calculator (Descriptive Stats, Z-Scores, Correlation, Regression). Compute descriptive statistics, z-scores, Pearson/Spearman correlation, or simple linear regression for a numeric dataset you supply. The 'operation' field selects one of four modes: 'describe' (single dataset), 'zScores' (single dataset), 'correlation' (two equal-length datasets), or 'linearRegression' (two equal-length datasets). Use this for analysing a list of numbers; use math_percentage_calculator for percent-of and percent-change math, or math_ratio_calculator for proportions. Runs locally on the numbers you provide: read-only, non-destructive, contacts no external service, and is rate-limited (60 requests/minute for anonymous callers). Returns a JSON envelope (success, operation, result) whose 'result' shape depends on the chosen operation; quartiles and percentiles use Type-7 linear interpolation, and excess kurtosis is reported (a normal distribution gives roughly 0).

Input Schema

TableJSON Schema

Name	Required	Description
`operation`	Yes	Mode selector. describe and zScores each need the values array; correlation and linearRegression each need both x and y arrays.
`values`	No	Numeric dataset for describe and zScores (required for those, ignored otherwise). 1 to 100000 finite numbers; numeric strings are coerced. NaN and Infinity are rejected.
`x`	No	First numeric dataset for correlation and linearRegression (the independent variable for regression). 2 to 100000 finite numbers; must be the same length as y.
`y`	No	Second numeric dataset for correlation and linearRegression (the dependent variable for regression). 2 to 100000 finite numbers; must be the same length as x.

Output Schema

TableJSON Schema

Name	Required	Description
`success`	No	Always true on a 200 response.
`operation`	No	Echo of the requested operation.
`result`	No	Operation-specific output (fields below are grouped by the operation that returns them).

Schema Changelog

Changes observed during successful MCP inspections.

Changed11 schema fields changedv0.5.1Jun 3, 2026

addedInput schema / additionalProperties
```
Added value: +false
```

addedInput schema / properties / operation / description

Added value: +"Mode selector. describe and zScores each need the values array; correlation and linearRegression each need both x and y arrays."

addedInput schema / properties / operation / enum

Added value: +[
+  "describe",
+  "zScores",
+  "correlation",
+  "linearRegression"
+]

addedInput schema / properties / values / description

Added value: +"Numeric dataset for describe and zScores (required for those, ignored otherwise). 1 to 100000 finite numbers; numeric strings are coerced. NaN and Infinity are rejected."

changedInput schema / properties / values / items / type
```
Previous value: -"integer"New value: +"number"
```
addedInput schema / properties / values / maxItems
```
Added value: +100000
```
addedInput schema / properties / values / minItems
```
Added value: +1
```

addedInput schema / properties / x

Added value: +{
+  "description": "First numeric dataset for correlation and linearRegression (the independent variable for regression). 2 to 100000 finite numbers; must be the same length as y.",
+  "items": {
+    "type": "number"
+  },
+  "maxItems": 100000,
+  "minItems": 2,
+  "type": "array"
+}

addedInput schema / properties / y

Added value: +{
+  "description": "Second numeric dataset for correlation and linearRegression (the dependent variable for regression). 2 to 100000 finite numbers; must be the same length as x.",
+  "items": {
+    "type": "number"
+  },
+  "maxItems": 100000,
+  "minItems": 2,
+  "type": "array"
+}

changedInput schema / required

Previous value: -[
-  "operation",
-  "values"
-]New value: +[
+  "operation"
+]

changedOutput schema / (root)

Previous value: -nullNew value: +{
+  "properties": {
+    "operation": {
+      "description": "Echo of the requested operation.",
+      "type": "string"
+    },
+    "result": {
+      "description": "Operation-specific output (fields below are grouped by the operation that returns them).",
+      "properties": {
+        "coefficientOfVariation": {
+          "description": "describe: sample stddev divided by mean; null when mean is 0.",
+          "type": [
+            "number",
+            "null"
+          ]
+        },
+        "count": {
+          "description": "describe: number of values in the dataset.",
+          "type": "integer"
+        },
+        "formula": {
+          "description": "linearRegression: human-readable model form, y equals m times x plus b.",
+          "type": "string"
+        },
+        "geometricMean": {
+          "description": "describe: geometric mean; null unless every value is positive.",
+          "type": [
+            "number",
+            "null"
+          ]
+        },
+        "harmonicMean": {
+          "description": "describe: harmonic mean; null unless every value is positive.",
+          "type": [
+            "number",
+            "null"
+          ]
+        },
+        "intercept": {
+          "description": "linearRegression: y-intercept b of the best-fit line.",
+          "type": "number"
+        },
+        "kurtosis": {
+          "description": "describe: excess kurtosis (normal distribution gives roughly 0).",
+          "type": "number"
+        },
+        "max": {
+          "description": "describe: largest value.",
+          "type": "number"
+        },
+        "mean": {
+          "description": "describe and zScores: arithmetic mean.",
+          "type": "number"
+        },
+        "median": {
+          "description": "describe: middle value (Type-7).",
+          "type": "number"
+        },
+        "min": {
+          "description": "describe: smallest value.",
+          "type": "number"
+        },
+        "mode": {
+          "description": "describe: most frequent values; empty when all values are unique.",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "n": {
+          "description": "correlation and linearRegression: number of paired points used.",
+          "type": "integer"
+        },
+        "outliers": {
+          "description": "describe: values beyond 1.5 times the IQR fences.",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "pearson": {
+          "description": "correlation: Pearson product-moment coefficient.",
+          "type": "number"
+        },
+        "percentiles": {
+          "description": "describe: Type-7 percentiles at p10, p25, p50, p75, p90, p95, p99.",
+          "properties": {
+            "p10": {
+              "description": "10th percentile.",
+              "type": "number"
+            },
+            "p25": {
+              "description": "25th percentile.",
+              "type": "number"
+            },
+            "p50": {
+              "description": "50th percentile.",
+              "type": "number"
+            },
+            "p75": {
+              "description": "75th percentile.",
+              "type": "number"
+            },
+            "p90": {
+              "description": "90th percentile.",
+              "type": "number"
+            },
+            "p95": {
+              "description": "95th percentile.",
+              "type": "number"
+            },
+            "p99": {
+              "description": "99th percentile.",
+              "type": "number"
+            }
+          },
+          "type": "object"
+        },
+        "quartiles": {
+          "description": "describe: q1, q2 (median), q3, and iqr (q3 minus q1).",
+          "properties": {
+            "iqr": {
+              "description": "Interquartile range (q3 minus q1).",
+              "type": "number"
+            },
+            "q1": {
+              "description": "25th percentile.",
+              "type": "number"
+            },
+            "q2": {
+              "description": "50th percentile (median).",
+              "type": "number"
+            },
+            "q3": {
+              "description": "75th percentile.",
+              "type": "number"
+            }
+          },
+          "type": "object"
+        },
+        "rSquared": {
+          "description": "linearRegression: coefficient of determination (R squared).",
+          "type": "number"
+        },
+        "range": {
+          "description": "describe: max minus min.",
+          "type": "number"
+        },
+        "rootMeanSquare": {
+          "description": "describe: quadratic mean (RMS).",
+          "type": "number"
+        },
+        "skewness": {
+          "description": "describe: Fisher-Pearson skewness.",
+          "type": "number"
+        },
+        "slope": {
+          "description": "linearRegression: slope m of the best-fit line.",
+          "type": "number"
+        },
+        "spearman": {
+          "description": "correlation: Spearman rank correlation coefficient.",
+          "type": "number"
+        },
+        "stdDevPopulation": {
+          "description": "describe and zScores: population standard deviation (sigma).",
+          "type": "number"
+        },
+        "stdDevSample": {
+          "description": "describe: sample standard deviation (s).",
+          "type": "number"
+        },
+        "sum": {
+          "description": "describe: sum of all values.",
+          "type": "number"
+        },
+        "values": {
+          "description": "zScores: the normalised input dataset.",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        },
+        "variancePopulation": {
+          "description": "describe: population variance (sigma squared).",
+          "type": "number"
+        },
+        "varianceSample": {
+          "description": "describe: sample variance (s squared).",
+          "type": "number"
+        },
+        "zScores": {
+          "description": "zScores: standardised score per value, (value minus mean) divided by population stddev.",
+          "items": {
+            "type": "number"
+          },
+          "type": "array"
+        }
+      },
+      "type": "object"
+    },
+    "success": {
+      "description": "Always true on a 200 response.",
+      "type": "boolean"
+    }
+  },
+  "type": "object"
+}

First observedv0.1.0May 31, 2026

TDQS

A4.6/5.0

Behavior5/5

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

Discloses that it runs locally, is read-only, non-destructive, does not contact external services, and is rate-limited (60 req/min). Also details return format (JSON envelope) and special algorithms (Type-7 linear interpolation for quartiles, excess kurtosis). These go beyond annotations which already indicate readOnlyHint and destructiveHint.

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 and front-loaded with the title and main purpose. It is concise yet includes essential details. A minor deduction for slight density but overall efficient.

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 complexity (4 parameters, output schema, annotations), the description covers purpose, usage guidelines, behavioral traits, return format, and algorithm specifics. It leaves no obvious gaps for an AI agent to correctly select and invoke the tool.

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 coverage is 100%, so baseline is 3. The description adds explanation of operation modes (e.g., 'describe' needs values array, correlation needs x and y) but largely repeats schema descriptions. No significant new parameter semantics beyond what 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 clearly states the tool computes descriptive statistics, z-scores, correlation, and linear regression, specifying it works on numeric datasets. It distinguishes from sibling tools math_percentage_calculator and math_ratio_calculator, providing a specific verb and resource.

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?

Explicitly states when to use this tool (analysing a list of numbers) and when to use alternatives (percent-of/percent-change math with math_percentage_calculator, proportions with math_ratio_calculator). Also explains how the 'operation' field selects among four modes.

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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