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# Shapes of distributions

CCSS.Math:

## Video transcript

so what I want to talk about now our shapes of distributions in different words we might use to describe those shapes so right over here let's see we're talking about Matt's cafe and we have different age buckets so this is a histogram here and in each bucket it tells us the number of guests that are in that age bucket so a lot of we don't have any guests that are under the age of 20 we have a reasonable number between 20 and 30 we have a lot of guests at 30 in that bucket between 30 and 40 reasonable number between 40 and 50 and then as we get older we have fewer and fewer guests so just when you look at something like this a distribution like this something might pop out at you it kind of looks like if you were to imagine this were an armadillo this would be the body of the armadillo and then what we see to the right would kinda looks like the tail of the armadillo and we actually use those types of words to describe distributions so this distribution right over here it looks like it has a tail to the right it doesn't have a tail to the left in fact we have no one under the age of 20 but here when we have a few people between 60 and 70 even fewer between 70 and 80 even fewer between 80 and 90 and you know it kind of keeps going like this this is a tail and it's on the right side it's a right tailed distribution so I'd call this distribution right tailed and I'm using Khan Academy exercises because it's a good way to see a lot of examples and and frankly you should too because it will help you test your knowledge but it's not left tail left tailed we would see a tail going like that and it frankly if you're left tailed and right tailed you're likely to be approximately symmetrical remember symmetry that you define a line of symmetry and one type of symmetry is one where if you were to wear both sides of that line of symmetry or kind of mirror images of each other you could fold over the line of symmetry and they'll roughly meet and this one does not meet that because if you were to say maybe there's a line of symmetry here you're trying to fold this over it wouldn't match up the two sides would not match up so I feel good saying that it is right tailed so let's see retirement of age of each guest well yeah these names aren't that great but let's actually see what they're saying they're saying by age they're telling us the number of guests so this is this is a number of guests at a Logan assisted living so we have a lot of guests that are between 60 and 70 years old or reasonable that are between 50 and 60 or 70 or 80 and this distribution actually looks pretty symmetrical if I were to draw a line of symmetry right down here right at around an age of you know I guess the line would be the right at an age of 65 I guess you could say all this is a bucket for ages 60 to 70 then you could flip it over and it looks pretty symmetrical not exactly this bucket doesn't quite match up to this one but it's pretty close these roughly match each other these roughly match each other so I feel good about saying it is approximately symmetrical now just to know what these other words mean skewed to the left or skewed to the right these actually have fairly technical definitions when you get further in statistics but I guess easier to process version of them are when you have a left tail you tend to be when you attend it when you are left tailed you also tend to be skewed to the left and when you are right tailed you tend to be skewed to the right another way to think about skewed to the left is that your mean is to the left of your median mode that might not make any sense to you you might just want to go after the tail if your left tail you're probably left skewed if your right tailed you're probably right skewed so let's keep going let's see if we can see let's se see another example so this is interesting this is not we were not given a histogram here we're not given a bar graph we're given a box and whisker plot which is really just telling us the different quartiles so just to remind ourselves this tells us the minimum of our data set the bottom of our range so the minimum value in our data set we have at least one 11 and then the maximum value of our data set we have at least 125 now this line right over here is the median the middle number is 21 and then the box defines the middle 50% of our numbers so it's kind of the meat of our the meat of our distribution so if we were try to visualize what this would look like as maybe a histogram and we don't know for sure because we might have a whole bunch of 11s but not so much that it skews this but we could have more than one but a distribution that this could match up with is something that looks like having a tail down here and then you kind of bump up here this is the meat of the distribution it kind of looks something like that and I can't draw because I'm doing this on the exercises right now but for something like that well something like that would have a tail to the left would have a tail to the left it has its its range goes you know fairly low to the left but it might not have a lot of values there if it had more values on the left side this box would have been shifted over because a larger percentage would have fit would have been on the left so to speak and so this one I feel pretty good about saying this is skewed to the left it's definitely not symmetrical if it was symmetrical the median would be would be pretty close to the center the box would be pretty centered and it's not skewed to the right if it was q' to the right you would have a tail to the right you would have this whisker would likely be much much much longer and we're done