# Sample quantile check

`sample-quantile-check` · version 1.0.0 · Numbers & math · free, no key needed

Check claimed quantiles or percentiles of an exact sample under Hyndman-Fan type 1-9; returns the first mismatch.

**Use when you need to: check claimed percentile of a sample · verify quartile values against data · validate quantile under hyndman fan type 7.**

## Decide before calling

Read the [versioned contract](/v1/tools/sample-quantile-check/versions/1.0.0) and the supported scope below. Reuse `sample-quantile-check@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `sample-quantile-check@1.0.0` for check claimed percentile of a sample. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- check claimed percentile of a sample
- verify quartile values against data
- validate quantile under hyndman fan type 7
- check nearest rank percentile claim
- audit excel percentile inc result
- confirm interquartile values for a data set

## Not supported

- weighted quantiles or quantiles of grouped data
- theoretical distribution quantiles (normal, t, chi-square)
- choosing a quantile definition for the caller
- Harrell-Davis or kernel quantile estimators

## Behavior

- Reference: Hyndman and Fan (1996) definitions 1-9 (the numbering used by R stats::quantile type = 1..9); reference_version is returned with every result.
- The sample (same rules as sample-summary-check: safe integers or ASCII decimal strings) is sorted into x(1) <= ... <= x(n), with x(k) = x(1) for k < 1 and x(k) = x(n) for k > n.
- Q(p) = (1 - g) x(j) + g x(j+1). Types 4-9: j = floor(np + m), g = np + m - j, m = 0, 1/2, p, 1 - p, (p+1)/3, p/4 + 3/8.
- Types 1-2: j = floor(np), h = np - j, g = 1 if h > 0 else 0 (type 1) or 1/2 (type 2). Type 3: j = floor(np - 1/2), g = 0 if np - 1/2 = j and j is even, else 1.
- p is an exact integer, decimal or p/q in [0, 1]; claims are checked in array order; duplicate p values (by value) are invalid_input.
- match (omitted = "exact"): "round_half_even_to_claim_digits" rounds the exact quantile half-to-even to the claimed value's written fractional digits; fraction claims stay exact.
- First mismatch: {index, p, claimed, actual, actual_rounded, lower_rank, upper_rank, weight} with the clamped ranks of x(j) and x(j+1) and g as an exact string.
- Numbers are returned in canonical exact form: integer, terminating decimal without trailing zeros, or reduced p/q.

## Input

- `sample` (array of integer or string, required): min items 1; max items 10000
- `method` (one of "type1", "type2", "type3", "type4", "type5", "type6", "type7", "type8", "type9", required)
- `claims` (array of object, required): min items 1; max items 200
- `match` (one of "exact", "round_half_even_to_claim_digits", optional)

## Output

- `valid` (boolean, required)
- `reason` (one of null, "quantile_mismatch", required)
- `first_discrepancy` (object or null, required)
- `claims_checked` (integer, required): min 0
- `method` (one of "type1", "type2", "type3", "type4", "type5", "type6", "type7", "type8", "type9", required)
- `reference_version` (string, required)

## Limits

- max sample items: 10000
- max value chars: 40
- max fraction digits: 30
- max claims: 200

## Example

Request input:

```json
{
  "sample": [
    15,
    20,
    35,
    40,
    50
  ],
  "method": "type7",
  "claims": [
    {
      "p": "0.4",
      "value": "29"
    }
  ]
}
```

Response:

```json
{
  "result": {
    "valid": true,
    "reason": null,
    "first_discrepancy": null,
    "claims_checked": 1,
    "method": "type7",
    "reference_version": "Hyndman and Fan (1996) sample quantile definitions 1-9, Am. Stat. 50(4):361-365; r60-sample-statistic-verifiers@1.0.0"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "sample-quantile-check",
  "version": "1.0.0",
  "input": {
    "sample": [
      15,
      20,
      35,
      40,
      50
    ],
    "method": "type7",
    "claims": [
      {
        "p": "0.4",
        "value": "29"
      }
    ]
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/sample-quantile-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"sample":[15,20,35,40,50],"method":"type7","claims":[{"p":"0.4","value":"29"}]}'
```

The machine-readable contract is at [/v1/tools/sample-quantile-check/versions/1.0.0](/v1/tools/sample-quantile-check/versions/1.0.0).

### CLI

```sh
node cli.mjs run sample-quantile-check 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Sample summary check](/tools/sample-summary-check): Check claimed count, sum, mean, median, range, variance or SD of an exact sample; returns the first mismatching field.
- [Sample histogram check](/tools/sample-histogram-check): Check claimed histogram counts, outside count and densities for exact edges and an edge rule; returns the first bad bin.
- [Network cut capacity check](/tools/network-cut-capacity-check): Check a claimed s-t cut: source-side membership, the edges crossing it and its capacity, with exact integers.
- [Network flow feasibility check](/tools/network-flow-feasibility-check): Check a claimed s-t flow for capacity bounds and conservation with exact integers; returns the first bad edge or node.
- [Coloring count check](/tools/coloring-count-check): Check a proper indexed coloring and an exact canonical-decimal claim for its number of distinct colors.
- [Linear residual check](/tools/linear-residual-check): Check a claimed residual r = b - A x (per component and/or its max norm) exactly for an approximate solution x.