Standard Deviation (SD15/SD24) (STANDARD DEVIATION)

Standard Deviation (SD15/SD24)

STANDARD DEVIATION

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Standard Deviation (SD) measures the statistical dispersion of IQ scores across population samples. Because modern tests map raw results to a relative bell curve (Mean = 100), the choice of Standard Deviation (either SD15 or SD24) dramatically changes the numerical output value for the exact same level of intelligence.

1. The Normal Distribution Bell Curve

Plotted globally, human intelligence follows a symmetrical standard bell curve. Under the standard SD15 metric:

±1 SD (IQ 85 to 115) houses 68.27% of the population.
±2 SD (IQ 70 to 130) houses 95.45% of the population.
Above +2 SD (IQ 130+) represents the top 2.28% of humanity (the gifted threshold).

2. Scale Comparison: SD15 (WAIS) vs. SD24 (Cattell/Mensa)

Standard clinical tests use SD15. Historical scales and some MENSA branches used SD24. They represent the exact same level of intelligence (percentile), but use different size markings:

Percentile Rank	Rarity Index	IQ Score [SD 15]	IQ Score [SD 24]
50.0% (Average)	1 in 2 people	IQ 100	IQ 100
15.8% (+1 SD)	1 in 6 people	IQ 115	IQ 124
2.28% (Gifted Limit)	1 in 44 people	IQ 130	IQ 148
2.0% (MENSA Limit)	1 in 50 people	IQ 131	IQ 150

Wechsler, D. (2008). Wechsler Adult Intelligence Scale—Fourth Edition (WAIS-IV). NCS Pearson.
Cattell, R. B. (1971). Abilities: Their structure, growth, and action. Houghton Mifflin.
Neisser, U., et al. (1996). Intelligence: Knowns and unknowns. American Psychologist, 51(2), 77-101.

❓ 関連するよくある質問 (FAQ)

Use the linear formula: $IQ_{24} = (IQ_{15} - 100) \times 1.6 + 100$. Thus, a clinical IQ 130 (SD15) converts to $30 \times 1.6 + 100 = 148$ (SD24).

Many casual online tests inflate scores by using arbitrary scales (like SD30 or SD36) or lack standardizing samples. Under standard SD15, the statistical ceiling is capped around IQ 160 due to sample limits.

Modern clinics, hospitals, and schools universally standardize WAIS and WISC cognitive reports using the standard SD15 index.

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