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export default function ZScoreComparison() { const testA = { mean: 50, sd: 10, score: 70, z: (70 - 50) / 10, }; const testB = { mean: 80, sd: 2, score: 84, z: (84 - 80) / 2, }; const scalePosition = (score, mean, sd) => { const min = mean - 4 * sd; const max = mean + 4 * sd; return ((score - min) / (max - min)) * 100; }; return (

Why We Standardize Scores

Two students took different math tests. Their raw scores look different, but z-scores help us compare them fairly.

Test A

Average score (μ) = 50

Standard deviation (σ) = 10

Alex's score (x) = 70

z = (70 - 50) / 10 = 2
{testA.mean - 4 * testA.sd} Average: {testA.mean} {testA.mean + 4 * testA.sd}

Alex is 2 standard deviations above average.

Test B

Average score (μ) = 80

Standard deviation (σ) = 2

Mia's score (x) = 84

z = (84 - 80) / 2 = 2
{testB.mean - 4 * testB.sd} Average: {testB.mean} {testB.mean + 4 * testB.sd}

Mia is also 2 standard deviations above average.

Main Idea

Even though Alex scored 70 and Mia scored 84, both students performed equally well compared to their own class averages.

Z-scores measure how unusual or impressive a score is relative to everyone else.
); } ⬅ Back to Home