Practice question · Put in order
Order the steps to standardize a raw score and turn it into a percentile.
- Divide that difference by the standard deviation to get the z-score.
- Subtract the mean from the raw score.
- Convert the z-score to a percentile using the empirical rule or a z-table.
- Note the sign: positive is above the mean, negative below.
Hints
- Standardizing (getting the z) must finish before any percentile lookup begins.
- The z-score itself is only a distance in SD units; turning it into a percentile is a separate final step.
Show the answer
- Subtract the mean from the raw score.
- Divide that difference by the standard deviation to get the z-score.
- Note the sign: positive is above the mean, negative below.
- Convert the z-score to a percentile using the empirical rule or a z-table.
Why
You compute the deviation, divide by the SD to get z, read its sign, and only THEN convert to a percentile. Skipping the last step - treating the z-number itself as a percentile - is the named pitfall of this lesson.
Practise The Normal Curve and Z-Scores
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