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Video transcript:

Hi, I’m Michael Corayer and this is Psych Exam Review and in this video I’m going to talk about some more descriptive statistics. So in a previous video I talked about the measures of central tendency and these tell us about the center of a distribution. But in this video I’m going to talk about measures of variance and what measures of variance tell us is how much scores vary.

So measures of variance tell us about the differences between scores. The simplest way is to look at the range. The range is a measure of variance that just tells us the distance between the lowest score and highest score. So if you took a test in class and the highest score was 90 and the lowest score was 70 then the range would be 20 because there’s 20 points between 70 and 90.

However, if you took a test and the highest score was 100 and lowest score was 20 in that case the range would be 80. So it just tells us how far apart the scores are from the lowest to highest. The problem with this is that it’s all about the extremes.

It’s sensitive to extreme scores because, by definition, the range is about the extreme scores. So you could take a test in class and if everybody scores within a few points of 80 then the range is just going to be a few points but as soon as one student scores a 20 then suddenly the range is going to increase dramatically.

So the problem we have is that we don’t know if that’s happened, we don’t know are the scores actually close together most of the time and there was one exception or were lots of scores really spread out. So to answer that question we need to look to another measure a variance. And this one is the standard deviation. And what the standard deviation tells us is how much each score varies from the average. So it involves taking each individual score and saying “how far away from the average was this score?” and then it takes the average of all of those distances. So the standard deviation tells us how scores vary from the mean. So it’s the average of all of the distances from the mean.

And this let’s us know, are scores really close together or are scores really spread apart. So if you took a test and the average score was 70, you might want to know, did most people score near 70? Or was it spread out? Some people scored really and some people scored all the way up to 100 and those would be very spread out.

So a small standard deviation means that all the scores were really close together near the mean and a large standard deviation means that they’re more spread out. So let’s look at how the standard deviation is calculated. And don’t worry you probably won’t ever have to calculate this by hand. But we should be able to make sense of this equation since we understand the concept of what the standard deviation is. So the standard deviation is the sum of each score compared to the mean and then it’s the average of all those distances.

So let’s make sense of this equation. So S here stands for standard deviation of a sample and sigma here just refers to the sum. X is our score, each individual score would be X. X-bar is our average, or our mean, and n is the number of scores that we have. So all this equation is saying is we compare each score to the mean and the reason we have this square here is because some of the scores are going to be the above the mean and some of the scores are going to be below the mean and when we subtract the mean from the score we’re going to end up with some negative numbers and we want to cancel those out, so we square them so that they’re not negative anymore. So we add all those differences up, and then we take the average of them, we divide it by the number of scores -1 and then since we squared earlier we have to take the square root of that sum in order to get the actual standard deviation.

Like I said, you probably won’t have to calculate this by hand, the important thing is you understand the concept. The standard deviation refers to how the scores vary from the mean. So we can have this sort of, let’s say we have some distribution of scores we have a mean here, we want to know are the scores of all right here really close to that mean or are the much more spread out and they cover a distance more like this, and that’s what the standard deviation will tell us. So smaller standard deviation, closer together, larger standard deviation, more spread out.

I hope you found this helpful. If so, please like the video and subscribe to the channel for more. Thanks for watching!