Hi. I am Doctor Shah. I was the National Lecture Competition winner in 1989 and I am the math master at math school. Now, ready for a new way of doing math? So there are three measures of average. The first one is the mode. The second one is the median. And the third one is the mean. The mode is the one which occurs most frequently. It is very easy to figure out the mode, but it is not very mathematical so we tend not to use it a lot. The median is the middle one in an ordered list so a lot more useful because it is identifying the middle of the data. So, that is what you expect of an average. And the last one is called the arithmetic mean. It is also sometimes referred to as the weighted average. Now, the reason it is referred to as the weighted average is this. Imagine you have got a workplace, and in that workplace, there are five staff and they all earn twenty thousand. There are also three managers and they earn thirty three thousand. And of course, there is the boss and he earns a whopping one hundred and sixty thousand. If we were working out the median of this data, we'd be looking for the middle one. We would cross out from each end till we got to the middle one which is this one here. So that would be the median. If we wanted to work out the mean, what we would be doing is adding them all up and diving by how many there are. So add them all up and divide by nine and when you do that you get an answer of forty thousand pounds. The weighted average is very different from the median because this one large number has a large weight on the data, on the average. And that is why it is called the weighted average. Each value is not just taken into account as being a value but also if it is a very big value it can effect the data a lot. And this would be a good example of where it would be better to use the median rather than the mean because you have an extreme value in that data. .

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