[MUSIC PLAYING] Hi, Dan Laub here. And in this lesson, we're going to talk about representing how data is normally distributed. And before we get started, let's talk about the key objective for this lesson. What we want to do is understand a normal distribution, and to be able to identify the mean, median, and mode when looking at a graph of a bell curve. So let's get started.
Now that you have some basic understanding of data and how it is measured, it is important to know how the data is distributed. Simply knowing the mean, median, or mode is generally not sufficient enough to explain much about the data. So knowing just how much the data strays away from those measures is important as well.
Knowing how data is distributed allows us to make predictions about what to expect and what not to expect for a given set of data. Graphically, smooth curves can be used to show the distribution of variables. And these curves are called density curves. Look at the graph you see on the screen. Notice how the curve is smooth and shaped like a bell.
What's useful about a density curve is that it shows us how often a given value was recorded. So again, taking a look at the curve, you'll see what happens in order to create this curve is that we take a large number of observations and plot them out as far as how often they happen. And we'll notice that eventually, we'll get some sort of shape that resembles a bell.
Looking at the bell curve you see in front of you, this represents IQ scores. And so an IQ score is essentially a measurement of how intelligent a person is. And you'll notice here that what we see at the bottom on the horizontal axis is going to represent the actual score. And we'll notice that the bell shaped curve is drawn above the horizontal axis, at it's centered at 100, which is the average IQ.
The range of this bell shaped curve goes from, at the low end on 40, and up to the high end at 160. This type of curve is called a normal distribution curve. And normal distribution curves occur quite often in many different situations.
The next graph I want to show you represents the time spent on social media per day by teenagers. And so what we're looking at in a graph like this is we see, once again, a bell shaped curve. And we see that the average, or the mean, is centered there at 500 minutes per day. We'll notice the range at the bottom of 200 minutes per day on the low end, and the high of 800 minutes per day on the high end.
And we'll notice the number. And so we have a hypothetical 10,000 teenagers, we'll notice that the numbers on the left-hand side. And we'll notice how the large number of observations are concentrated more toward the center. And so when we're looking at normal distributions, they all have density curves that are symmetric and bell shaped. And the mean, median, and mode of the normal distribution are all the same and equal to the center value of the density curve, which in this case is 500.
So 500 is the average, 500 is the mode, and 500 is the median. Which means it's the largest number of observations. It's also the point at which half of the observations are greater than and half are lower than. Let's look at a couple other examples here just to get a sense of what the normal distribution curve looks like.
The next one I want to show you is going to be the height of college basketball players. This graph indicates the distribution of the height of college basketball players. And so we'll notice, once again, it's a bell shaped curve. We'll notice that the mean, median, and mode is 77 inches, which is what, 6 foot 5 inches tall. And we'll notice how the distribution is relatively narrow. We'll notice how most of the players are clustered right around that midpoint. So there's not a whole lot of variation from that actual mean right there of 77 inches.
The last graph I want to look at is a distribution of SAT scores. So the average in this case is 1,497, which was actually the average SAT score in the year 2012. So right around 1,500. And we'll notice how it deviates a little further. And what happens is the curve looks a little flatter in this particular instance, and the right and left-hand sides kind of stray a little bit further from that mean and median and mode. And so we get a little bit wider distribution with regard to how the observations actually fall.
The objective of this lesson was relatively simple. It was to understand what a normal distribution is, which we covered, and to be able to identify the mean, median, and mode when looking at a graph of a bell curve, which we did. It's going to be that center point at the very top of the bell curve that has the most observations, the point at which is the average, and the point at which half the observations are greater than or half are less than. So again, my name is Dan Laub. And hopefully, you got some value from this lesson.
(0:00 - 0:33) Introduction
(0:34 - 1:29) Bell Shaped Curves
(01:30 - 2:06) Normal Distributions
(2:07 - 4:06) Measures of Center
(4:07 - 4:30) Conclusion
Source: Graphs created by Dan Laub.