Sample summary check
sample-summary-check · version 1.0.0 · Numbers & math · free, no key needed
Check claimed count, sum, mean, median, range, variance or SD of an exact sample; returns the first mismatching field.
Use when you need to: check claimed sample mean and variance · verify descriptive statistics claim · validate reported standard deviation against data.
Decide before calling
Read the versioned contract and the supported scope below. Reuse sample-summary-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-summary-check@1.0.0 for check claimed sample mean and variance. 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 sample mean and variance
- verify descriptive statistics claim
- validate reported standard deviation against data
- did the agent compute the median correctly
- check sample vs population variance claim
- audit summary statistics of a list of numbers
- confirm sum min max range of a sample
Not supported
- computing statistics without a claim (use a statistics compute tool)
- weighted, trimmed or grouped-data statistics
- skewness, kurtosis or mode
- floating-point tolerance comparisons other than half-even rounding to the claimed digits
Behavior
- Reference: NIST/SEMATECH e-Handbook of Statistical Methods (2012) 1.3.5.1 (mean, median) and 1.3.5.6 (variance, standard deviation, range); reference_version is returned with every result.
- sample: 1-10000 items, each a JSON safe integer or an ASCII decimal string (no exponent or plus sign, <= 30 fractional digits, <= 40 characters); non-integer JSON numbers are rejected.
- Exact rationals: mean = sum/n; median = middle order statistic or the mean of the two middle ones; range = max - min; sum_squared_deviations = sum (x - mean)^2; variance = that / (n-1) or / n; standard_deviation = sqrt(variance).
- variance_denominator ("n-1" or "n") is required when variance or standard_deviation is claimed, otherwise optional and unused; "n-1" with n = 1 gives valid false, reason statistic_undefined.
- Claims are integers, decimals or p/q fractions compared by exact value; count is a non-negative JSON integer.
- match (omitted = "exact"): "round_half_even_to_claim_digits" rounds the true value half-to-even to each decimal claim's written digits; fraction claims and count stay exact.
- standard_deviation: exact mode needs a rational sqrt equal to the claim; rounding mode compares the correctly rounded integer-square-root result. Irrational sqrt gives actual null and actual_rounded at the claim digits (30 for a fraction claim).
- Fixed comparison order count, sum, min, max, range, mean, median, sum_squared_deviations, variance, standard_deviation; the first mismatch is returned as {field, claimed, actual, actual_rounded} with reason <field>_mismatch.
- actual is canonical: integer, terminating decimal without trailing zeros, or reduced p/q.
Input
sample(array of integer or string, required): min items 1; max items 10000claim(object, required)variance_denominator(one of "n-1", "n", optional)match(one of "exact", "round_half_even_to_claim_digits", optional)
Output
valid(boolean, required)reason(one of null, "count_mismatch", "sum_mismatch", "min_mismatch", "max_mismatch", "range_mismatch", "mean_mismatch", "median_mismatch", "sum_squared_deviations_mismatch", "variance_mismatch", "standard_deviation_mismatch", "statistic_undefined", required)first_discrepancy(object or null, required)checked_fields(array of one of "count", "sum", "min", "max", "range", "mean", "median", "sum_squared_deviations", "variance", "standard_deviation", required): max items 10reference_version(string, required)
Limits
- max sample items: 10000
- max value chars: 40
- max fraction digits: 30
Example
Request input:
{
"sample": [
2,
4,
4,
4,
5,
5,
7,
9
],
"variance_denominator": "n",
"claim": {
"mean": "5",
"variance": "4",
"standard_deviation": "2"
}
}Response:
{
"result": {
"valid": true,
"reason": null,
"first_discrepancy": null,
"checked_fields": [
"mean",
"variance",
"standard_deviation"
],
"reference_version": "NIST/SEMATECH e-Handbook of Statistical Methods (2012) 1.3.5.1 + 1.3.5.6; r60-sample-statistic-verifiers@1.0.0"
}
}How to call it
MCP
Connect https://computefirst.net/mcp (setup), then call execute with:
{
"id": "sample-summary-check",
"version": "1.0.0",
"input": {
"sample": [
2,
4,
4,
4,
5,
5,
7,
9
],
"variance_denominator": "n",
"claim": {
"mean": "5",
"variance": "4",
"standard_deviation": "2"
}
}
}HTTP (no key)
curl -X POST https://computefirst.net/v1/tools/sample-summary-check/versions/1.0.0/execute \
-H "Content-Type: application/json" \
-d '{"sample":[2,4,4,4,5,5,7,9],"variance_denominator":"n","claim":{"mean":"5","variance":"4","standard_deviation":"2"}}'The machine-readable contract is at /v1/tools/sample-summary-check/versions/1.0.0.
CLI
node cli.mjs run sample-summary-check 1.0.0 --input input.json --base-url https://computefirst.netGet the client at /clients/cli/.
Related tools
- Sample quantile check: Check claimed quantiles or percentiles of an exact sample under Hyndman-Fan type 1-9; returns the first mismatch.
- Linear residual check: Check a claimed residual r = b - A x (per component and/or its max norm) exactly for an approximate solution x.
- Lp primal feasibility check: Check that a claimed LP point satisfies x >= 0 and Ax <= b exactly; report the first violated bound or row.
- Network cut capacity check: Check a claimed s-t cut: source-side membership, the edges crossing it and its capacity, with exact integers.
- Sample histogram check: Check claimed histogram counts, outside count and densities for exact edges and an edge rule; returns the first bad bin.
- Coloring count check: Check a proper indexed coloring and an exact canonical-decimal claim for its number of distinct colors.