Constructing distributions from simulations

0:00- [Instructor] We're told for a simulation, Naja uses this spinner. Naja spins the spinner 200 times, all right? What is the random variable in this simulation? What are its possible values? Well, the random variable is going to be the result of the spinner. So, the result of each spin is the random variable.

0:24We could give that some type of a variable like an X. Usually, a random variable uses a capital letter, like a big X or a big Y. But that's the result of each spin is the random variable. And what are its possible values? Well, the possible values are A, B or C.

0:40A, B or C. Now, in this next part, it's asking us, "Complete the relative frequency table to show the results of her simulation." And we have to remember that she spins the spinner 200 times. They told us that up here. So, based on that, let's see if we can complete this table.

1:01And if you feel so inspired, which I always encourage you to feel, pause this video and try to do it yourself. Okay, so, if she landed in sector A, 0.27 of the time, or 27 out of a hundred times or 27% of the time, she had 200 spins. So, 27% or 27 hundredths of 200 is 54, I should say.

1:30And how did I get that? I just multiplied that by the number of spins, or another way to think about it if you had to go the other way, 54 out of 200 is equal to 0.27. And actually, we can use that to skip to part C right over here. If she got 96 C's out of 200, then the frequency right over here would be 96 over 200, which is the same thing as 48 over 100, which is the same thing as 48 hundredths.

2:01Now, last but not least, we can figure out the entries for B, one, 54, 96 and whatever B is need to add up to 200 and 0.27, 0.48 and whatever the B frequency is needs to add up to one. So, let's look at it over here. 96 plus 54, six plus four is 10, so this is 150.

2:27So, what do I have to add to it to get to 200? I have to add another 50 right over there. And then, what's the frequency of 50 out of 200? Well, 50 out of 200 is zero point, 50 out of 200 is one-fourth, so 0.25. And we can verify that if you add all these numbers up, 0.27 plus 0.25, that would be 0.52.

2:58And you add that to 0.48. That indeed does equal one. And then last but not least, they are asking us show the results of her simulation by constructing an appropriate data display. So, let me do that. Well, I'll do it relatively small, I used up all the space over here.

3:18But I think I have space to do it. There's multiple data displays you could do. I can imagine doing a pie graph that actually would look a lot like the spinner, but I'll do a bar graph here. So, let's say right over here on the vertical axis, so, well, on the horizontal axis, let's put the possible outcomes of the spin.

3:37So, you have A, B or C. And in the vertical axis, we could put count or we could put frequency. I'll put count over here. So, our count, it goes up to a hundred. So, let's say it is 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100. So, that's a hundred. And let's see, 90, this is 80, this is 60, this is 40, this is 20 over here.

4:09And if I want, I could make it similar colors. If I look at the original, A is in that blue color, B is in that yellow color, C is in that salmon color. So, I'm not gonna match the colors exactly. But A, we get 54 out of the 200. So, 54, this is 50, 54 would get us right about there.

4:30So, that is the bar for A. And then for B, we had 50 out of 200. So, B, 50 is right over here. That would look like this. It would look like that. That's the bar for B. And then C is 96 out of 200. So, C is going to look something, it's not the exact color, but close enough.

4:57I'll use this pink. 96, that's 90, 96 is right about there, right about, that is obviously hand-drawn. You could use some type of chart-making software to do this much more exact. But this is a pretty good data display, a bar graph in this case to see the relative counts, or to see the counts of the different outcomes of the random variable.