What is the meaningful difference between someone with a 145 IQ compared to a 100 IQ?
I am a lay person and new to this, and while I do understand that 145 IQ means 3 SDs up from the mean, I want to have a rough idea of what it means in real-life examples, from people who have experience in this domain. What is it that a person with a 145 IQ can typically do that a persona with a 100 IQ can typically not do? Examples of feats or the like is appreciated.
The answer about three standard deviations is correct. But you cannot state that someone is 45% smarter. Makes no sense. Nominal, ordinal, interval and ratio are the types of scales used, and IQ is an interval scale with no zero point (an IQ of zero does not mean no intelligence like zero pounds of flour means none). Ask a mathematician why it takes a true zero point for that.
I don't think it is correct to use "intelligence" and "IQ" as synonyms. IQ tests measure IQ, that is, they measure the thing that they measure. "Intelligence" is undefined or has many definitions, and has many dimensions.
I can't find the source I read it from, hence this isn't an actual answer, but I remember reading somewhere that the further up the IQ scores you go, the more reliant on speed it is and the less reliant on difficulty. Once you've got all the questions in your test right, you're arguably no more clever than anyone else who also got all the questions right within a reasonable timescale. The subtle difference in the speed at which you arrive at a sound solution is a different metric to the ratio of sound to unsound solutions you arrive at.
As a general note, precision in measurement of intelligence declines as you move to more extreme levels. There is greater uncertainty in measurement in the 145 range than there is at the 100 range. Norm samples get smaller, and most measures of intelligence are designed for the normal range.
Categories: You might find the article on IQ classification useful. The article discusses a wide range of ways to give verbal labels to IQ scores. For example, the following categories would put a 145 IQ person above "very superior" intelligence.
Statistical interpretations: You correctly note that 145 represents 3 standard deviations above the mean. If you assume a normal distribution and no measurement error, IQ 100 means you are more intelligent than 50% of the population, and an IQ of 145 means you are more intelligent than 99.9% of the population. Or to put another way, 1 in 2 people have an IQ greater than 100, and roughly 1 in 750 people have an IQ of greater than 145.
Intuition: If you went to a large representative high school (say with 500 to 1000 students), you might think of the typical student as your 100 IQ student, and the smartest kid in school as possibly being in the 145 ball park.
Another way to get some intuition is to think about the typical range IQs for various professions. As you see below, even for professions with the most intelligent people are still typically well below 145.