Final answer:
IQ scores on tests like the Stanford-Binet and the Wechsler scales tend to follow a normal distribution, represented by a bell curve, with most scores near the average of 100 and fewer toward the extremes. A score within one standard deviation (85 to 115) is average, whereas scores that are two standard deviations away from the mean may indicate different levels of intellectual ability.
Step-by-step explanation:
When scores on IQ tests like the Stanford-Binet and the Wechsler scales are examined, they approximate a normal distribution, which is a symmetrical, bell-shaped curve, with a majority of scores falling in the middle of the possible range and few scores appearing toward the extremes. This distribution reflects the bell curve. On most IQ tests, the average (or mean) score is set at 100, and the scores are spread around this mean. Most people have an IQ score between 85 and 115, which is considered average, encompassing 68% of the population according to the empirical rule. Scores that fall more than two standard deviations below the mean, which would be about 70 on most scales, may indicate an intellectual disability, while a score of 130 or above is considered indicative of superior intelligence or 'giftedness.'
The term standard deviation is critical to understanding the bell curve in IQ testing. With 15 points being one standard deviation in these tests, a score of 115 is described as 'one standard deviation above the mean,' while a score of 70 is described as 'approximately two standard deviations below the mean.' It is these standard deviations that allow us to understand an individual's score in relation to the population average and broader distribution of intelligence across the population.