IIF Certified Assessment
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IIF Certified Assessment
Drag anywhere on the curve. Switch to compare mode to see what sits between two scores — and whether the gap between them is real.
Drag on the chart to move the marker. Hover to read any point.
| Range | Share of people | Note |
|---|---|---|
| 85 – 115 | 68.3% | One SD either side of the mean |
| 70 – 130 | 95.4% | Two SD |
| 55 – 145 | 99.7% | Three SD — the reportable range |
| 100 – 110 | 24.8% | A 10-point gap at the middle |
| 120 – 130 | 6.8% | The same 10 points, at the shoulder |
| 135 – 145 | 0.8% | The same 10 points, in the tail |
Set two scores to compare them.
The curve is steepest in the middle, which is why most people cluster there and why the same number of IQ points means less and less as you move outward.
68.3% of people. One standard deviation either side of the mean. Two thirds of the population sits inside this 30-point stretch.
95.4% of people. Two standard deviations. Almost everyone you will ever meet scores somewhere in this range.
2.3% of people, about 1 in 44. This is where high-IQ societies set their thresholds — Mensa uses the 98th percentile.
2.3% of people. A single online result at this level says very little on its own and should never be treated as a diagnosis.
About 1 in 741. Past this point the curve is extrapolation — real tests have too few people at the extremes to measure it reliably.
IQ 100 is the 50th percentile by construction. Tests are standardised so the population mean is fixed at 100, at every age.
Because the curve is not flat, an identical gap covers a completely different share of people depending on where it sits.
Ten points near the middle separates a quarter of everyone. The same ten points out at the edge separates fewer than one person in a hundred. It is the same distance on the number line and a completely different distance in the population.
Because IQ tests are deliberately built that way. Raw scores are converted so the population mean sits at 100 and the spread follows a normal distribution with a standard deviation of 15. The bell shape is a property of how the scale is constructed, not a discovery about the brain.
About 68.3% of people score between 85 and 115, which is one standard deviation either side of the mean. Roughly 95.4% score between 70 and 130, and about 99.7% between 55 and 145.
Because the curve is tallest in the middle. Moving from 100 to 110 passes 24.8% of the population, while moving from 135 to 145 passes only 0.8%. The same distance on the scale covers a very different share of people depending on where it sits.
Usually not. Because every score carries measurement error, two results only differ reliably when the gap is larger than about 1.96 times the standard error of the difference. On a test with a reliability of .90 that threshold is roughly 13 points, so a 10-point gap is within the range you would expect from noise alone.
Because beyond roughly three standard deviations the normal curve is being extrapolated rather than measured. Standardisation samples contain very few people at the extremes, so rarity figures past that point describe the mathematical model and not an observed count.
Not exactly. The scale is constructed to be normal, and it fits well through the middle, but the lower tail carries more very low scores than the model predicts because some causes of severe impairment sit outside normal variation. Treat the curve as a good working model rather than a literal description.
Take the assessment to get a measured score, its percentile, and where it actually falls on this distribution.
