// ============================================================================
// Descriptive statistics — mean, variance, stddev, median via sort
// ============================================================================
//
// Mean is sum/len. Variance is the mean of squared deviations. Median sorts
// the sample and takes the middle (or the average of the two middles for an
// even count). All of it rides on list reductions and bracket indexing.
//
//   soma run statistics.cell run
// ============================================================================

cell Statistics {
    face {
        signal mean(xs: List) -> Float
        signal variance(xs: List) -> Float
        signal stddev(xs: List) -> Float
        signal median(xs: List) -> Float
        signal run() -> Map
    }

    on mean(xs: List) {
        return to_float(sum(xs)) / to_float(len(xs))
    }

    on variance(xs: List) {
        let m = mean(xs)
        let sq = xs |> map(x => (to_float(x) - m) * (to_float(x) - m))
        return sum(sq) / to_float(len(xs))
    }

    on stddev(xs: List) {
        return sqrt(variance(xs))
    }

    on median(xs: List) {
        let s = sort(xs)
        let n = len(s)
        let mid = floor(n / 2)
        if n % 2 == 1 {
            return to_float(s[mid])
        }
        return (to_float(s[mid - 1]) + to_float(s[mid])) / 2.0
    }

    on run() {
        let xs = [2, 4, 4, 4, 5, 5, 7, 9]
        return map(
            "mean", mean(xs),
            "variance", variance(xs),
            "stddev", stddev(xs),
            "median", median(xs)
        )
    }
}

cell test StatTests {
    rules {
        // mean of 2,4,4,4,5,5,7,9 = 40/8 = 5
        assert mean([2, 4, 4, 4, 5, 5, 7, 9]) == 5.0
        // textbook population variance = 4, stddev = 2
        assert abs(variance([2, 4, 4, 4, 5, 5, 7, 9]) - 4.0) < 0.0000001
        assert abs(stddev([2, 4, 4, 4, 5, 5, 7, 9]) - 2.0) < 0.0000001
        // odd-count median
        assert median([7, 1, 3]) == 3.0
        // even-count median averages the two middles
        assert median([1, 2, 3, 4]) == 2.5
    }
}