About this video
The mean is one common way to describe the centre of a data set, and it is what people usually mean by "average". To find it, add all the values and divide by how many values there are: the books read (5, 8, 11, 7, 6) give 37 divided by 5, which is 7.4. The mean can also be seen as the balance point if equal weights are placed on a number line at each value.
You'll be able to
- calculate the mean of a data set by adding the values and dividing by how many there are.
- explain that the mean is a measure of centre and is what people usually call the average.
- describe the mean as the balance point of the data.
Key words
- mean
- The sum of all the values divided by the number of values.
- average
- The everyday word people usually use when they mean the mean.
- centre of data
- A single number that describes where the middle of the data is.
- data point
- One value in a data set, like one student's number of books.
- balance point
- The place on a number line where equal weights at each data value would balance; it is the mean.
Transcript
- [Instructor] We're told the following table shows the number of books read by each student during a reading challenge, all right? And then it says find the mean number of books read. Now, first of all, we just have to think about what does mean mean? So when we're looking at data, statisticians, mathematicians have always said, "Okay, I have a bunch of data, are there ways to represent all of that data maybe with a single number?"
And maybe one way to do that is to try to get some notion of where the center of that data actually is. Now, as you'll see in future videos, there's many ways of defining the center of data, but the mean is definitely one of the most common. In everyday language, when people say average, they're usually talking about the mean.
Later on, you'll see there's other more mathy ways or other ways of defining it, but usually when people say the average, they're talking about the mean. So to calculate the mean, we essentially want to take the sum of all these numbers and divide by the numbers we actually have.
So the mean of this data is going to be five plus eight, plus 11, plus seven, plus six, and then that's going to be divided by, I have one, two, three, four, five data points. So let's see, five plus eight is 13, plus 11 is 24, plus seven is 31, and then plus six is 37.
Let's see. Did I do that right? Let me go this way, make sure I get the same answer. Six plus seven is 13. Yeah, this is 13, that's 13, 36. Yep, this is all going to be 37. So five goes into 37, so this is, I could write it as a fraction. It goes into it seven times with the remainder of two, so seven and two fifths.
Or we could, if you want to turn two fifths into a decimal, that's 0.4. So this is 7.4. Another way to think about it, if you're more of a visual person, you like to visualize things, is imagine that I had this, let's call it some kind of a platform, but it has no weight to the actual platform.
And let me put some numbers on it, all the way up to 11. Actually, I could just even start at, start at five, five, six, seven, eight, nine, 10, and then 11. And I'm gonna put a weight for each of these. So Danica is at five. So I'm gonna put a, let's say a one pound weight there.
Liam is at eight. I'm gonna put a one pound weight there. Rhone is at 11. I'm gonna put a one pound weight there. Jamal is at seven. I'm gonna put a one pound weight there. Patricia is at six. And if I were to say intuitively, where would I put something, if you wanted to hold it with one finger and balance this whole thing, where would you put it?
And you might intuitively say, "Oh, I'd put my finger right around here to balance everything." And so if you did it and if you actually balanced it, that balance point you would see is actually right at 7.4. So that's another interesting thing that this measure of center, the mean, does for us.
Another way to conceptualize it.
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