In this video I cover descriptive statistics and three measures of central tendency; the mean, median, and mode. The calculation of each is explained, as well as potential problems, such as the mean’s sensitivity to extreme scores, especially in small samples. I also discuss the possibility of multimodal and uniform distributions.
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*I should clarify the example of a multimodal distribution that I used, the scores of 90 and 84 should be out of a larger group of students (more than 10) with other scores also occurring. If 90 and 84 were both the most-frequent scores then they would both be modes. If 90 and 84 were the only scores and they occurred equally then this would be a uniform distribution. Sorry for any confusion!
Video transcript:
Hi, I’m Michael Corayer and this is Psych Exam Review and in this video I’m going to talk about descriptive statistics and these are statistics that simply describe the data that we’ve collected. And we’re going to look at three measures of central tendency. So these are three different types of statistics that tell us about the central tendency of our data. The first of these you’re probably familiar with and that is the mean or the average.
So the mean is calculated by adding up all of our scores so it’s the sum of scores divided by the number of scores.
And you’ve probably calculated an average before but let’s look at an example. Let’s say that I give 10 students a test and nine of those students earn a 90 on the test and one student earns a 0 on the test.
Well let’s find the average. So I’m going to have 90 plus 90, plus 90, plus 90, plus 90, nine times plus zero so that’s gonna give me 810. Then I’m going to divide by the total number of students, which is 10 students and so we can see in this case the average is gonna be 81.
Now you can see the problem with using the mean. The problem here is that it’s very sensitive to this 0. This 0 has a very strong effect. You know until that was there, you know, the average would have been 90 and then one 0 brings it all the way down to 81.
So what’s going to happen is if I tell the students when I give their test back, I say the average score was 81 I’ll have nine students who think they did “better than average” when in fact each of them only did better than one other student.
So the problem with the mean is that it’s sensitive and it’s sensitive to extreme scores. So when we have a very high or very low score the mean is gonna be affected very strongly and this is especially true if we have a small sample size.
So because I only had 10 students this effect was very noticeable. If I had 1000 students and one student got a zero then it wouldn’t affect the mean very much but because we have such a small sample only 10 students, it had a very strong effect.
So another measure of central tendency that doesn’t have this problem is the median. And the median is simply the middle score. So to find the median all we have to do is we line up our data in order, so we put each score in order and then we just find which one is right in the middle.
So imagine I gave people some sort of test and they had some number as their score so let’s say 2, 4, 5, 7, 8.
So let’s say these are the scores that we’re looking at in these five people and what we do is we line them up and then we just look which score is in the middle of this list and it’s 5. So in this case the median would be 5.
And we can see that here it’s not so sensitive to extreme scores because I can go in and change one of these scores I could say imagine if instead of 8 what if the highest score was all the way up at 80? Totally far away from these other scores.
Well, in that case, the median would still be 5. It wouldn’t be influenced by the fact that this score was extremely high.
You might wondering how do I find the median if I have something like this, let’s say 2, 4, 5 and let’s throw in another score, 6,
Ok so what if this is my distribution of scores, you might look and say what do I do, 5 and 6 are both in the middle? You know I have an even number of scores so there is no middle. And all you do in that case is you add the two middle scores so that would be 5+6 and you divide by 2, you take the average of these two and so in that case our median would be 5.5
Ok, so that’s the median, it’s much less sensitive to extreme scores. Again I could go in and change this to 80 here and this wouldn’t change at all. And the last measure of central tendency that we’ll look at is the mode.
And the mode is the most frequent score. And so to find the mode all we do is we look at all of the scores and we count how many times did each score occur. So if we go back to our first example, we see okay 90 occurred nine times and zero occurred one time and so 90 was the most frequently occurring score and so 90 would be the mode.
Now you might ask, “well what I do if if I have more than one most frequent score?” and that’s possible and we call that a multimodal distribution. So for instance if I had 10 students take an exam and five of them scored 90 and five of them scored 84 then when I calculate the mode, I’d say the mode is 90 and the mode is also 84, so you can have more than one mode.
And you might also ask, “what do I do if none of the scores is most frequent? What if I look and each score occurred only one time. Like in this example here, you might say what’s 2, 4, 5, 7, 80, what’s mode in this case? In this case all of them are the mode or you could say none of them are the mode. And the way of saying that is saying it’s a uniform distribution and that just means that each score was equally frequent.
So in that case all of the scores occurred once so it’s a uniform distribution. If each of the scores had occurred twice, it would still be called a uniform distribution.
So those are the three measures of central tendency I hope you found this helpful. If so, please like the video and subscribe to the channel for more.
Thanks for watching!
