Round #1013
19 May 2026, 10:23· math· Meta-Llama-3.3-70B-Instruct· r13-clean-hints
- Complexity
- band 0
- ZP / UO / OBS
- 3 / 0 / 0
- Journey weight
- 255
- Lightshift ΔL
- —
Prompt
Given the data set {4, 8, 6, 5, 3, 7, 8}, compute the mean, median, and mode.
Zero-point index (what the engine surfaced)
ZPI-ZPI-0010 | 2026-05-19T10:23:22Z
Given the data set {4, 8, 6, 5, 3, 7, 8}, compute the mean, median, and mode.
ZERO POINT — 3 entries (structural invariants)
● hsl(191.58, 100%, 15%) arithmetic mean Σx_i / n [contract]
● hsl(175.07, 100%, 15%) median: middle value of ordered sample [contract]
● hsl(27.26, 100%, 15%) mode: most frequent value [contract]
UNOBSERVED — 0 entries (implied truths)
OBSERVED — 0 entries (explicit in request)
COMPLEXITY │ 3 entries │ spread: 0° │ band: LOW
Baseline response (no ZPI)
```csharp
using System;
using System.Linq;
class Program
{
static void Main()
{
// Define the dataset
int[] data = { 4, 8, 6, 5, 3, 7, 8 };
// Compute the mean
double mean = data.Average();
Console.WriteLine("Mean: " + mean);
// Compute the median
Array.Sort(data);
double median;
if (data.Length % 2 == 0)
median = (data[data.Length / 2 - 1] + data[data.Length / 2]) / 2.0;
else
median = data[data.Length / 2];
Console.WriteLine("Median: " + median);
// Compute the mode
var groups = data.GroupBy(x => x).OrderByDescending(x => x.Count());
int mode = groups.First().Key;
Console.WriteLine("Mode: " + mode);
}
}
```
Enhanced response (with ZPI)
```csharp
using System;
using System.Linq;
public class StatisticsCalculator
{
public static void CalculateStatistics(int[] data)
{
// Calculate mean
double mean = data.Average();
Console.WriteLine($"Mean: {mean}");
// Calculate median
Array.Sort(data);
double median;
int n = data.Length;
if (n % 2 == 0)
{
median = (data[n / 2 - 1] + data[n / 2]) / 2.0;
}
else
{
median = data[n / 2];
}
Console.WriteLine($"Median: {median}");
// Calculate mode
var groups = data.GroupBy(x => x).OrderByDescending(x => x.Count());
int mode = groups.First().Key;
Console.WriteLine($"Mode: {mode}");
}
public static void Main(string[] args)
{
int[] data = { 4, 8, 6, 5, 3, 7, 8 };
CalculateStatistics(data);
}
}
```
This C# code calculates the mean, median, and mode of a given data set. The `CalculateStatistics` method takes an array of integers as input, calculates the mean using the `Average` method, the median by sorting the array and finding the middle value, and the mode by grouping the data by value and finding the most frequent value. The results are then printed to the console. The `Main` method demonstrates how to use this method with a sample data set.
Grader chain
Each grader reads the same baseline + enhanced pair and casts an independent verdict. Disagreement is the framework's own signal — not noise to be averaged away.
V1samba/Meta-Llama-3.3-70B-Instruct
BetterV4qwen2.5-coder-3b-instruct
BetterV5cerebras/qwen-3-235b-a22b-instruct-2507
SameV7qwen2.5-coder-7b-instruct
SameV8openai/gpt-4.1
BetterV9anthropic/claude-opus-4-7
SameV12openai/gpt-4o
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