Free tool
Turn a raw score into a z-score and a percentile on the normal curve, or work backward from a z-score or percentile to the raw score. Defaults to the IQ scale: mean 100, standard deviation 15.
Built for Intro PsychologyEnter the known values.
Z-scores, standard deviations and the bell curve come up in research methods and in intelligence testing. Encodr keeps both on a spaced-repetition schedule.
Get started freeA z-score says how many standard deviations a score sits from the mean: z = (x - mean) / sd. Working
backward, x = mean + z x sd. A positive z is above the mean and a negative z is below it.
On a normal (bell) curve, the percentile is the share of scores below x, read from the standard normal distribution. As a rule of thumb, about 68% of scores fall within 1 standard deviation of the mean, about 95% within 2 and about 99.7% within 3. The calculator gives the exact figure for your z.
Worked example: modern IQ tests are scaled to a mean of 100 and a standard deviation of 15, so a score of 115 has z = (115 - 100) / 15 = 1, which is the 84.13th percentile. A score of 85 has z = -1, the 15.87th percentile. Going backward, the 97.5th percentile has z = 1.96, which is an IQ of about 129.4. The full explanation is in z-scores and percentiles explained, and the whole course is in the free Intro Psychology deck. If your data come from measurements with uncertainty, the error propagation calculator covers that side of statistics.
What a z-score is, how to turn it into a percentile on the normal curve, and how the 68-95-99.7 rule works, with IQ examples from intro psychology.
What an Intro Psychology course covers, unit by unit, from research methods and the brain to learning, memory, disorders and therapy, with real card counts.
How to study for Intro Psychology - applying terms to scenarios, separating look-alike concepts, learning classic studies and stage theories, and spacing.
Forgetting isn't a study failure. It's a predictable process, and once you can predict it, you can schedule around it.
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