About this video
Two basketball teams' points per game are shown in dot plots. By pairing values on either side, the video finds the Panthers' mean is 54 and the Bulldogs' mean is 50, with the same spread. It then checks each statement and concludes the Panthers typically scored more points per game.
You'll be able to
- estimate the mean of a symmetric dot plot by looking at its centre.
- use the mean to compare what is typical for two groups.
- tell the difference between comparing centres and comparing consistency.
Key words
- dot plot
- A graph that shows each data value as a dot above a number line.
- mean
- A measure of centre found by adding all the values and dividing by how many there are.
- typical
- A value that describes what usually happens; the mean is one good way to measure it.
- consistent
- Scoring close to the centre every time, which means the data has a small spread.
- spread
- How far apart the values in a data set are from each other.
Transcript
- [Instructor] We're told that two basketball teams recorded the number of points they scored in each game during a season. The results are shown in the dot plots and they say each dot represents the number of points scored in a game. So for example, it looks like the Panthers had one game where they scored 54 points, two where they scored 55, four where they scored 56, and then we can do the same type of analysis for the Bulldogs.
So they're asking us, "Which statement is true about the two teams' points per game?" Pause this video and have a go at this before we do it together. All right, let's look at 'em one by one. "The Bulldogs had a higher mean than the Panthers." So, a mean is a measure of center, and what you would normally do is add up all of the values and then divide by the number of values.
Now we're not, we don't have to do all of that. We can actually just visually inspect where the mean is likely to be here. Because if I took the average of this and this, I would end up here, halfway in between 'em. If I took the average of this and this, halfway between.
Between this and this, still end up there. The average of that and that, I'd still end up here. The average of that and that, I'd still end up there and then the average of that and that, I'd still end up here. So we know that our mean, right over here, averages, when people say it in everyday language, they're usually talking about the mean.
We have a mean here of, we have a mean here of 54. Of 54. And by that same logic, we have a mean here of, we have a mean of 50. That's the mean for the Bulldogs. So the Bulldogs definitely did not have a higher mean than the Panthers. They had a lower mean. "The Bulldogs were more consistent than the Panthers."
Consistency would mean you're scoring close to the center, maybe close to the mean every time, but their spread, in fact, these distributions look identical except they're shifted. So they're actually similarly consistent. The Bulldogs would be more consistent if instead of these dots being over here, if they were, maybe these four were over here.
One, two, three, four, then that would be more consistent and if these four were one, two, three, four, you would have a tighter spread, but that's not what we see here. "Both teams had the same typical number of points per game." No, typical number of points per game.
One way to think about typical or a good way to think about typical is the actual mean. There's other ways of thinking about typical, but it's not the same. This one, the mean for the Bulldogs is definitely lower. "The Panthers typically scored more points per game than the Bulldogs."
Yeah, their mean is noticeably higher, so I like that choice.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.