Interpreting variability

0:00- [Instructor] Two dart-throwing robots are being tested for how consistently they hit a target. The results are shown in the dot plots and each dot represents the distance in centimeters from the bullseye for one throw. So, I don't know, maybe a positive number is to the right or to the left.

0:14I guess this is a circular bullseye, but, well, let's just say where (chuckles) can be to the right or the left of this thing. And so we have the two distributions and now they are asking us which statement is true about the two robots' performance. So pause this video, have a go at that before we do this together.

0:32All right. Statement A says Robot X is more consistent because the data has a greater spread. So, it is true that the word consistent, if something is consistent, it normally has less... (finger taps) We are told two dart-throwing robots are being tested for how consistently they hit a target.

0:59The results are shown in the dot plots. Each dot represents the distance in centimeters from the bullseye for one throw, and I guess they're measuring to the right or the left. That's why we can have these negative numbers or these positive numbers. I'll just assume that.

1:11Now, they're giving us a bunch of statements and we have to pick which one is correct, so pause this video, have a go at that before we do this together. All right, let's go through each of these statements. Robot X is more consistent because the data has greater spread.

1:27Now, that doesn't sound right, because if you are more consistent, more consistent, that's not because you have greater spread, it's because, and this is a two-way arrow, you have less spread. So Robot X actually is more consistent, because if you notice its spread, they both hit the target exactly three times.

1:53So they hit the target exactly three times. Now, Robot X has four that were one less than the target, I guess we could say one to the left, and then it has four hits that were to, one to the right. While Robot Y, you may say, "Okay, they only had two of each of those, but the other two were actually even further away."

2:17If these were over in this column right over here, then they would be equally consistent, but the ones that are not there are further away, so Robot Y is less consistent because it has more spread. So let's see. We know it's not that one. Robot Y is more consistent because the data has greater spread.

2:37It does have greater spread, but it's actually less consistent. Both robots are equally consistent? Nope, that's not right. Let's see. Because they are both centered around the same distance from the bullseye. It is true that their means, both of these look like their means will be right at hitting the bullseye, but that doesn't talk about consistency.

2:55They might have the same mean, but Robot Y is definitely less consistent. Robot X is more consistent, yep, because the data has a smaller spread. Yep. We like that one.