Standard deviation in context
At about 38-43s the narrator describes standard deviation as 'the mean of the squares of the distance from that mean', which is the variance; standard deviation is its square root. Interventions avoid testing this wording.
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Two teams play a music game. Tap Trackers have a mean of 83.2 points and a standard deviation of 10.2; Pulse Players have a mean of 75.7 and a standard deviation of 5.8. The video uses the mean to judge a typical score and the standard deviation to judge consistency, concluding that Tap Trackers score higher on a typical try but Pulse Players are more consistent.
You'll be able to
- use the mean to compare typical values of two groups.
- use the standard deviation to compare how consistent two groups are.
- explain why a higher mean doesn't mean every member scored higher.
Key words
- mean
- The average value; a measure of the centre or a typical score.
- standard deviation
- A measure of spread: roughly how far scores are from the mean on average.
- consistent
- Having scores that stay close together, shown by a low standard deviation.
Transcript
- [Instructor] We're told that, "Each of the 40 members on two teams receives a score from a music game. The mean for the Tap Trackers team is 83.2 points and the standard deviation is 10.2 points." Let's see, this is Tap Trackers right over here. Mean is 83.2, which is right about there.
So this is the mean. So right over here, standard deviation is 10.2 points. Remember, standard deviation is a measure of spread. How far from the mean on average are you? This is the average... The mean of the squares of the distance from that mean. "The mean for the Pulse Players team is 75.7 points."
So it's lower. 75.7 would be right around here, all right? "And the standard deviation is 5.8." So they have a lower mean, but they have a lower mean and a lower standard deviation. So they have a lower, I guess, if you view mean as a form of average, they have a lower central tendency, but they're also less spread apart because they have a lower standard deviation.
One way to think about it is they're more consistent. So let's look at the choices here 'cause they're gonna ask us some questions. "Choose the correct comparison of scores for each team." And you can pause the video and have a go at this before I do this. "Pulse Players score higher on a typical try, but Tap Trackers score more consistent."
Let me see. It's actually the Tap Trackers that score, they have a higher mean, so that's definitely not right. This one, A, implies that Pulse Players have an higher mean. Higher mean, that's not true. Tap Trackers, higher mean. They do have a higher mean. "Guarantees that every member scored higher than Pulse Players."
No, that's not true even if we didn't see the data. But when we look at the data we can see that there's definitely people on the Tap Trackers who scored lower than other people on the Pulse Players. Just 'cause your mean is higher doesn't mean that every player is better than the other team.
"Pulse Players lower standard deviation," yep, they have, they do have a lower standard deviation, "shows that they typically score higher." No, that doesn't make sense. Standard deviation is a measure of spread, not how high or low you are, not your central tendency.
So it's probably going to be D, but let's just verify that and read it. "Tap Trackers score higher on typical try." Yep, that makes sense 'cause they have a higher mean. "But Pulse Players scores are more consistent." Yes, they have a lower standard deviation.
They're not quite as far spread apart. So I will pick D and we're done.
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