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# Visually assessing standard deviation

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.J (LO)
,
UNC‑1.J.3 (EK)
CCSS.Math:

## Video transcript

each dot plot below represents a different set of data we see that here order the dot plots from largest standard deviation top to smallest standard deviation bottom so pause this video and see if you can do that or at least if you could rank these from largest standard deviation to smallest standard deviation all right now let's work through this together and I'm doing this on Khan Academy where I can move these around to order them but let's just remind ourselves what the standard deviation is or how we can perceive it you could view the standard deviation as a measure of the typical distance from each of the data points to the mean so the largest standard deviation which we want to put on top would be the one where typically our data points are further from the mean and our smallest standard deviation would be the ones where it feels like on average our data points are closer to the mean one all of these examples our mean looks to be right in the center right between fifty and a hundred so right around seventy-five so it's really about how spread apart they are from that and if you look at this first one it has these two data points one on the left and one on the right that are pretty far and then you have these two that are a little bit closer and then these two that are inside this one right over here to get from this top one to this middle one you essentially are taking this data point and making it go further and taking this data point and making it go further and so this one is going to have a higher standard deviation than that one so let me put it just like that and I just want to make it very clear keep track of what's the difference between these two things here you have this data point and this data point that was closer in and then if you move it further that's going to make your typical distance from the middle more which is exactly what happened there now what about this one well this one is two starting here and then taking this point and taking this point and moving it closer and so that would make our typical distance from the middle from the mean shorter so this would have the smallest standard and this would have the largest let's do another example so same idea ordered the dot plots from largest standard deviation on the top to small a standard deviation on the bottom pause this video and see if you can figure that out so this is interesting because these all have different means just eyeballing it the mean for this first one is right around here the mean for the second one is right around here at around 10 and the mean for the third one it looks like the same mean is this top one and so pause this videos how would you order them alright so just eyeballing it these this middle one right over here your typical data point seems farthest from the mean you definitely have if the mean is here you have these this data point and this data point that are quite far from that mean and even this data point and this data point are at least as far as any of the data points that we have in the top of the bottom one so I would say this has the largest standard deviation and if I were to compare between these two if you think about how you would get the difference between these two is if you took this data point and moved it at and you moved it to the mean and if you took this data point and you moved it to the mean you would get this third situation and so this third situation you have the fewest data points that are sitting away from the mean relative to this one and so I actually like this ordering that this top one has a largest standard deviation and this bottom one has the smallest standard deviation
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