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# Frequency tables & dot plots

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

## Video transcript

what I have here is the list of ages of the students in a class and what I want to explore in this video is different ways of representing this data and then see if we can answer questions about the data so the first way we can think about it is as a frequency table frequency table frequency table and what we're going to do is we're going to look at each for each age for each possible age that we've measured here see how many students in the class are of that age so we could say the age is one column and then the number the number of students of that age or we could even say the frequency frequency when people say how frequent do you do something they're saying how often does it happen how often do you do that thing frequency or we could also say actually I'm just right number I'm always a fan of the simpler number at age which we could also consider the frequency at that age frequency of students all right so what's the lowest age that we have here well the lowest age is five so I'll start with five and how many students in the class are age five how frequent is the number five let's see there is one two let me keep scanning looks like there's only two fives so I could write a two here there are two fives and now let's go to six how many sixes are there let's see there is one six there's only one six-year-old in the class all right seven year-olds see there's one two three four seven year-olds for seven year olds now what about eight year olds eight year olds I'm going to do this in a color that I have not used yet eight year olds we have no eight year olds zero eight year olds and then we have nine year olds let's see nine year olds we have one two three four nine year olds for nine year olds ten year olds what do we have have one ten-year-old right over there and then 11 year olds 11 year olds there are no 11 year olds and then let me scroll up a little bit and then finally 12 year olds 12 year olds there are one to twelve year olds so what we have just constructed is a frequency table it's a frequency table you can see you can see for each age how many students are at that age so it's giving you the same information as we have up here you could take this table and construct what we have up here you would just write down two fives one six four sevens no eights four nines one 10 no 11s and two twelves and then you wouldn't just have this list of numbers now a way to visually look at a frequency table you could is a dot plot so let me draw a dot plot right over here so a a dot plot and a dot plot we essentially just take the same information and even think about it the same way but we just show it visually so in a dot plot what we would have and the dot plot what we would have of actually I would let me just not draw any venero there we have the different age groups so 5 6 7 8 9 10 11 and 12 and we have a dot to represent or we use a dot for each student at that age so there's two five year olds so I'll do two dots one and two there's one six-year-old so that's going to be one dot right over here there's four seven year-olds so one two three four dots there's no eight-year-olds there's four nine year olds so one two three and four there's one ten year old so let's put a dot one dot right over there for that one ten-year-old there's no eleven year old so I'm not going to put any dots there and then there's two twelve year olds so one twelve year old and another 12 year old so there you go we have frequency table dot plot list of numbers these are all showing the same data just in different ways and once you have it represented in any of these ways we can start to ask questions about it so we could say what is the most frequent age well the most frequent age when you look at it visually though or the easiest thing might be just look at the dot plot cuz you see it visually the most frequent age are the two highest acts so there's actually seven and nine our free are tied for the most frequent age you would have also seen it here where seven and nine are tied at four and if you just had this data you would actually need have to count all of them to kind of come up with this again and say okay there's four sevens four 9s that's the largest number so this is if you're looking for what's the most frequent age when you just visually inspect here probably pops out at you the fastest but there's other questions we can ask ourselves we can ask ourselves what is the range what is the range of Ages in the classroom and this is once again where maybe the dot plot is the most it jumps out at you the most because the range is just the maximum age in your or the maximum data point minus the minimum data point so what's the maximum age here well the maximum age here we see it from this from the dot plot is 12 and the minimum age here you see is five so there's a range of seven the difference between the maximum and the minimum is seven but you could have also done that over here you can set a the maximum age here is 12 minimum age here is five and so subtract from Twitter from five you said you find the difference between 12 and 5 which is 7 here you do not have to do it you could still kind of done it except what's the lowest let's look at 5 are there any fours here no there's no 4 so 5 0 mage and what's the larger says it 7 knows it 9 9 9 10 12 12 are there any 13s no 12 is the maximum so you say 12 minus 5 is 7 to get the range but that we could ask ourselves other questions we could say how many how many older older than 9 is a question we could we could ask ourselves and then if we were to look at the dot plot we say ok this is 9 and we care about how many are older than 9 so that would be this 1 2 & 3 or you could look over here how many are older than 9 what's the one person who's 10 and then the two who are 12 so there are three and over here if you said how many are older than 9 you well then you would just have to go through the list and say okay no no no no no no no okay here 1 2 3 into the knot that person right over there so hopefully you this is just an appreciation for yet another two ways of looking at data frequency tables and dot plots