Now in this section we're going to look at measures of central tendency, mean, median, and mode. We're going to represent all our data value that is with a single value. And let's start off with mean. Now, it's also known or more commonly known as the average. In most papers though, you'll see it written as the mean. It's probably the most commonly used parameter or statistic. Remember, if it's the whole population, it would be a parameter, if it's just a sample, it'll be a statistic. And it really is also the simplest to calculate. We're simply going to sum up all the values and we're going to divide by how many values there are. So let's look at this, Mgelea and colleagues, they published a report on Detecting Virological Failure in Tanzanian children. And in the results section you'll see for the 218 children, they quoted a mean age of 10.6 years. So instead of listing all of those 218 values, I mean depending on how large the font is it might take a few pages. And of course if a human being looks at all of those values, really will not make any kind of sense, but we can represent all of those with one value, the mean. Now we can complicate things a little bit, I mean mean is easy to do, you can complicate it a little bit. We can have weighted means, that's where we regard some of the values more important than, we would say that they're more important than others. So we might multiply every other value by two, certain values by two. We just have to remember then to add two to the number that we divide by. Now median, let's move onto median. Kristen Donald and her colleagues, we looked at this before, looked at the HIV Encephalopathy and they quoted a median age of 64 months. Now what do we do with a median? We really just take those values just at face value, actually. And we're going to select a value for which half of the values are less than that value and half of the values are more than that value. Let's look at a simple example. You see the numbers there, 3, 4, 5, 8, 10, 12, and 63. Now, look at that number 8, three of the values are less than 8, three of the values are more than 8, irrespective really of what they are. So the median for that set would be 8. Now, if you were to calculate the mean, that would be 15. And really, almost all the values, all the values but one is less than 15. Only one is more than 15, so is 15 really a true representation of that set? I think not. Now, you would also notice there that there were an odd number of values. What if there's an even number of values. If we throw away that 8 value now, we would take the middle two, now it becomes 5 and 10, and we're simply gonna take the mean. So, 10 plus 5 is 15, divided by 2 is 7.5. So the median of that set will now be 7.5. If we looked at the mean, now that would be 16.2, it's even worse. If you look at those values, 16.2 really is not a good representation of those, median would be much better. So, why do we use median there? Look at that value 63, as soon as you have a few values that are way different from the others, we call them statistical outliers, it's much better to use the median. Let's move on to mode, mode just tells us what value occurred most often. So we really use it with categorical data, the value that occurred most often. So let's consider this cross sectional survey study with pain scale. You can choose between 1, no pain, and 10, most pain, and imagine there were 16 participants and you see their choices there. Now we could add all of them and divide by 16 we could get to a mean of 5.6, but what is a pain value 5.6. It really makes no sense whatsoever, that's why we always say those are not numerical data type. Here we would rather use the term mode, 4 appears most often. The mode for this data set is 4 and it's a true representation, that is the pain value most patients suffered. Consider then also the likert scale, remember that? We had strongly disagree, disagree, neither agree nor disagree, nor agree. And there again it would be proper to use the mode, which of those choices most people choose. Now, unfortunately, in some data sets, there's not going be a single mode. Sometimes there're two values that occur as much as each other, and there we would call it bi-modal. It could even have more than just two, and there we'll call it multi-modal. In the next section, we're going to look at the dispersion of data.