In this video I describe variation in IQ scores and the distribution of IQ scores in the general population. IQ scores follow a normal distribution with a mean of 100 and a standard deviation of about 15 points. Knowing IQ follows a normal distribution allows us to estimate percentile scores for IQ and see how a particular score compares with all other scores. Intellectual giftedness (IQ scores around 130 and above) is associated with a number of positive life outcomes including greater longevity, while ‌intellectual disability (IQ scores below 70) is associated with difficulties completing routine daily tasks and inability to lead an indepedent life.

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Video Transcript

Hi, I’m Michael Corayer and this is Psych Exam Review. In this video I’m going to talk about IQ variation. So IQs vary, people get different IQ scores and in terms of assessment this is a good thing. This is what we want. Remember I said if we had an IQ test where everyone got the same score then it wouldn’t really be telling us anything about those people. So we want to be able to differentiate people. We want to see that they do have different abilities and different skills, and so a good IQ assessment will give us a broad range of different scores.

Now in doing this and making these finer distinctions between people, we might wonder if we’ve created some artificial distinctions. So we might wonder if there’s a practical difference between people with slightly different IQ scores. So for instance if a person scores 102 on an IQ test and another person scores 104, we might wonder if there’s really a practical difference in their abilities or not. At the same time, we could wonder about the fact that many people will have the same IQ scores. So if we pick an IQ score like 100, you know, which is the average IQ score then there will be lots and lots of people who have that same exact score. But of course that doesn’t mean that those people all have identical cognitive abilities.

So we’ll think about how other ways people differ might influence how they apply that intelligence and that’s something that we’ll look at when we talk about personality traits in the next unit. Ok, so if we were to look at all of the IQ scores for a particular assessment this would tell us the distribution of IQ scores in a population. So what does the distribution of IQ scores look like?

Well, if we look at the distribution of IQ scores, we find that it follows a normal distribution and this is something that I talked about in the chapter on research methods. So you might want to review that video but basically this is the idea that you have the mean, the median, and the mode all at the center of the distribution and it’s symmetrically distributed on either side. So what that means is that for IQ the mode, which is the most common score, is 100 and that means that’s also the average score. So if you add up all the scores and divide by the number of people that gives you the mean and in the case of IQ it will also be a 100. And we also have the median, which is 100, so in a normal distribution all of these are the same. And in the case of IQ they’re all 100. So the median score, again, is if you line up all the scores in order and then you pick the one that falls exactly in the middle, then in the case of IQ that would be 100.

Ok, we can also calculate a standard deviation for IQ and for IQ the standard deviation is about 15 points. So to refresh your memory on standard deviation, this is the idea that it tells us how different each score is from the average score. So you know some people are going to score very close to 100, there’s going to be a small difference from 100, other people are going to score farther away from 100. They’re going to be much higher or much lower than 100 and then what you do is you take the average of all of those differences. So you look at how much each score differs from 100 then you average all of those differences and in the case of IQ that will give you a standard deviation of about 15.

Ok, so let’s take a look at a chart here showing this. Ok, so here’s our normal distribution for IQ scores and what you can see is we have the score of 100 here which is the most frequent, right? So this is the score on this axis here and there’s not an axis drawn here but this is the frequency of that score. So this is a frequency distribution. We can see that the most common score, the highest frequency is 100, and that is also going to be the mean and the median because if we look the scores are symmetrical on either side so the middle point is going to be right here at 100. Ok, so as we move away, you know, one standard deviation will be here, that’s 15 points below, two standard deviations below will be here, three would be here. And on the other side we have the same thing. This would be one standard deviation, this would be two, and this would be three. And of course, there’s a, you know, this these tails continue off of the picture here.

But ok, so let’s take a look at what this means in terms of interpreting somebody’s score. So if we’re looking at somebody’s score on this, how do they compare to the rest of people who have taken an IQ test? Well, we look here between a score of 85 and 100, so this section of the line here, this section of people. This is going to be about 34% of people, that’s what I’ve labeled down here. So about 34% of the population will score between 85 and 100. That’s one standard deviation. Now on this side the same is true, in a standard deviation above the mean about 34% of people will score between 100 and 115. What that means is that you can look at this total section from 85 to 115 and that means you’re going to have about 68% of people score in that range. So the majority of people are going to score between 85 and 115 on an IQ test. Nearly 70 percent. Now if we extend to another standard deviation out here we say okay what about going all the way from 85 down to 70? We see that that’s going to be about 13.5 percent of people will score in this range and the same is true over here for this 115 to 130, 13.5 percent of people will score between 115 and 130 on an IQ test. And so we can again take a look at this whole section here from 70 all the way up to 130 and that means we’ll have about 95 percent of people in that range.

So almost everyone is going to score between 70 and 130 on an IQ test but you can see there’s still a few people left here at the very extremes here. So when we get below 70 we now have only about 2% of people will score below this, below 70 and higher than 55 so in this range here and then on the other side above 130 up to 145 we’ll have about 2 percent of people and that means again if we add up all of these scores so from 55 to 145 we’ll have pretty much everybody in the population at that point we’ll have 99.7% of people. Now I know with these numbers it doesn’t add up to exactly 0.7 but these are estimates so it’s about 99.7 and then that means that at the very extremes here we have like 0.1% maybe a little more, maybe a little less, of people score below 55 and like 0.1% of people score above 145. So if you hear somebody tell you, you know, their IQ is a 200 or something, they’re probably lying. I mean it’s possible but very, very unlikely. It’s a very very small fraction of the population that scores above 145.

And another important point about these is not only are these really small percentages of the population at these extremes but that it’s very unreliable at this point. It’s very hard to measure people once they get you know 3 standard deviations above or below the mean. Now in the case of very high IQ you can see that, you know it’s somebody scoring 160 or so you might wonder, well, who’s creating the test that they can really tell, you know? How do you design questions for somebody who’s really that brilliant and how can you do it in a reliable way so if they took the test again where they get the same score and that’s actually unlikely to happen when people get really really high scores here. They take the test again they might have a big change in their score. They’ll probably still be quite high but it’s less reliable at the extremes and the same is true down here and it’s maybe a little bit easier to think about when you think about being below 55 and wonder, well, how can you really differentiate people at that point? I mean the difference between 50 and 45 this is the point where, you know, you can barely get people to, you know, follow any instructions, you know? There’s going to be very, very little that they’re able to do and so to be able to differentiate people in terms of different skills at that point, it’s going to be very difficult. And those scores are also going to be unreliable.

Ok, so that’s our overall distribution of IQ scores and I’ve also sort of given you this idea of percentile score. So when you get a percentile score that tells you how many people are to the left of you on this graph. So if you were to look at this and say okay I scored 100 on an IQ test so I’m right here, what’s my percentile score? Your percentile score will be well how many people scored lower than you? And since you’re right at the middle here you know it’s 50% so you’d be at the 50th percentile. Whereas if you go over here, you say, okay I scored a 115 on an IQ test, what percentile is that? And that would be about the 84th percentile.

So you basically going through and adding up to be 34, plus 34, plus 13.5, plus 2, plus 1 everybody to the left. That would be about 84% of people to your left and that means you’d be at the 84th percentile. And so when you get way out here, you know, at, you know, 145 or something, then you’re at like the 99.9 percentile. Alright, very, very high whereas when your IQ scores below average then you’re going to be at a lower and lower percentile, right? If you’re at, you know, 70, you’re going to be, you know, around the second or third percentile. Ok, so that’s the idea of percentile scores and if you’ve taken the SAT before you’ve probably gotten the percentile score and that’s essentially telling you where you are on the distribution. What point are you on this line? Are you here, are you here, etc.? Ok, so that’s the idea of percentile score. Alright, so what do IQ scores mean? What can we say about the variation in IQ? Well, well we’ll start with thinking about what high IQ means.

So as I’ve said in a previous video there are several positive outcomes that are associated with higher IQs. It’s correlated to a number of things and these include better academic performance; people with higher IQs are more likely to achieve higher levels of education. They’re more likely to have higher status jobs. They’re more likely to earn more income and they’re more likely to do better at their jobs or they’re more likely to have higher job performance ratings. Alright, so these are all positive outcomes that are correlated with high IQ. Now you might wonder about this and say well you know these things all seem to be related to each other, right? All of these things that you’re predicting, so we can say that high IQ is a good predictor of future success. But you might say well okay it helps you get good grades, and those good grades help you get into a good college, and then getting into a good college gives you better job opportunities, and those better job opportunities allow you to earn more money, and so maybe that’s just all comes down to a high IQ helped you get good grades and that might be partly true. I mean these things are correlated with each other, you know, if you have higher education level then you’re going to probably earn more money.

You’re going to probably be able to do a more complex job but IQ is also associated with some things that you might not think it’s associated with, you might be surprised by. And one of these is greater longevity. And so here, you know, you couldn’t really use that argument and say well you know good grades help you live longer or something. So what is this, what is this about? What is, what’s causing this greater longevity associated with higher IQ? People with higher IQs tend to live longer than people with lower IQs, so what could be causing this?

Well one explanation might be that they have better “system integrity” meaning that whatever it is about their physical body that, you know, is related to their higher IQ is also better able to survive longer or something. Or it could be the case that they’re better at managing their health. So it might be the case of people who are higher IQ are better able to avoid accidents or they’re better at preventing diseases, you know, through certain behaviors that they they might practice or a certain knowledge that they might gain, might allow them to avoid disease more effectively than other people.

Or it could be the case that they have better access to resources, because of their higher job status, higher income, they might be better able to get access to health resources. And it’s probably not just one of these things that explains all this, it’s probably a combination of all of these factors. And one thing that we’ll look at in the chapter on stress is we’ll think about how people’s role in society actually influences their longevity in terms of their position in the social hierarchy. So people who are higher status, who have higher status jobs, tend to live longer and they tend to experience less stress. So that’s something that would be likely to be related to this higher IQ correlation but that’s something that I’ll come back to in the unit on stress. Ok, so when we look at the extremes of IQ,

we do have some terms for talking about them. And so in the case of high IQ, the extremes would be considered anything over about two standard deviations above the mean. So for IQ that would mean that somewhere around 130, scores that are higher than 130, that’s two standard deviations above the mean, would be considered giftedness. So intellectual giftedness. Now there’s not actually a precise score for defining giftedness but when we talk about people with higher IQ often we’re talking about this sort of higher extreme, this level of intellectual giftedness. But it’s not saying that, you know, if you score 129 then you’re not gifted, if you score 130 then you are. There’s not a precise value that defines it. But people who score in this range tend to generally have fulfilling lives and they tend to be well-adjusted and this goes against some stereotypes that people might have about very high IQ.

So they might think that people with very high IQ are not socially adjusted, they don’t have friends, they don’t get along with others, they’re sort of lonely and more likely to become depressed or things like that. And that’s generally not the case for people with higher IQ. They tend to be fairly happy and well-adjusted and lead meaningful lives.

Now we have the other extreme of low IQ and this is defined as intellectual disability and the previous term that you probably heard is mental retardation but that’s not really used anymore. And the definition for intellectual disability would be an IQ score below 70 and that’s two standard deviations below the mean or lower. And this is a range where people start having problems with completing everyday tasks. They may not be able to care for themselves and we’ll talk about intellectual disability a little bit more in the next video. We’ll talk about what causes these differences in IQ. Why is it that some people score in the IQ range that they do? And I won’t have a full answer to that question, but we will look at some possible causes of intellectual disability and what that means for those people.

So that’s an overall summary of variation in IQ scores; how people differ and the distribution of IQ scores in the population. I hope you found this helpful, if so, please like the video and subscribe to the channel for more. Thanks for watching!