Z Value Calculator

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Z-Value Calculator

Resulting Z-Value:

function calculateZScore() { var x = parseFloat(document.getElementById('rawScore').value); var mu = parseFloat(document.getElementById('popMean').value); var sigma = parseFloat(document.getElementById('stdDev').value); var resultContainer = document.getElementById('zResultContainer'); var output = document.getElementById('zOutput'); var interpretation = document.getElementById('zInterpretation'); if (isNaN(x) || isNaN(mu) || isNaN(sigma)) { alert('Please enter valid numeric values for all fields.'); return; } if (sigma 0) { text += "above the mean."; } else if (zScore < 0) { text += "below the mean."; } else { text = "This score is exactly equal to the mean."; } interpretation.innerHTML = text; resultContainer.style.display = 'block'; }

What is a Z-Value?

A Z-value (also known as a Z-score or standard score) is a statistical measurement that describes a value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

The Z-Score Formula

To calculate a Z-value, use the following formula:

z = (x – μ) / σ
  • x: The raw value (the score you are testing).
  • μ: The population mean.
  • σ: The population standard deviation.

Why is the Z-Value Important?

Z-values allow researchers and data analysts to compare scores from different data sets that might have different scales or units. By "standardizing" the scores, you can determine how unusual or typical a specific data point is compared to the rest of the distribution.

Practical Example

Imagine you took a math test and scored an 85. The class average (mean) was 70, and the standard deviation was 10.

  1. Subtract the mean from your score: 85 – 70 = 15.
  2. Divide the result by the standard deviation: 15 / 10 = 1.5.
  3. Your Z-value is 1.5. This means you scored 1.5 standard deviations above the average student.

Interpreting Results

  • ✅ Positive Z-score: The value is higher than the mean.
  • ❌ Negative Z-score: The value is lower than the mean.
  • ⚪ Z-score of 0: The value is exactly average.
  • 📊 Z-score > 3 or < -3: The value is often considered an outlier (very rare).

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