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# Statistics intro: Mean, median, & mode

AP.STATS:
UNC‑1 (EU)
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UNC‑1.I (LO)
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UNC‑1.I.1 (EK)
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UNC‑1.I.2 (EK)
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UNC‑1.I.3 (EK)
CCSS.Math:

## Video transcript

we will now begin our journey into the world of statistics which is really a way to understand or get our head around data so statistics is all about data and as we begin our journey into the world of this of of statistics we will be doing a lot of what we can call descriptive statistics so if we have a bunch of data and if we want to tell something about all of that data without giving them all of the data can we somehow describe it with a smaller set of numbers so that's what we're going to focus on and once we build our toolkit on the descriptive statistics then we can start to make inferences about that data start to make conclusions start to make a judgments and will start to do a lot of inferential inferential statistics make inferences so with that out of the way let's think about how we can describe a data so let's say we have a set of numbers we can consider this to be data maybe we're measuring the heights of our plants in our garden and let's say we have six plants and the heights are four inches three inches one inch six inches and another one's one inch and then another one is seven inches and let's say someone just said in another room not looking at your plants just say well you know how tall are your plants and they only want to hear one number they want to somehow hear get somehow give have one number that represents all of these different heights of plants how would you do that well you'd say well how can I find something that maybe I want a typical number maybe I want some number that somehow represents the middle maybe I want the most frequent number maybe I want the number that somehow represents the center of all of these numbers and if you said any of those things you would actually have done the same things that the people who first came up with descriptive statistics said they said well what how can we do it and we'll start by thinking of the idea of average average and in every day in every day terminology average has a very particular meaning as we'll see when many people talk about average going about the arithmetic mean which we'll see shortly but when we in statistics average means something more general it really means give me a typical give me a typical or give me a middle give me a middle number or these are ORS and really it's an attempt to find a measure of central tendency central central tendency tendency so once again you have a bunch of numbers you're somehow trying to represent these with one number we'll call it the average that somehow typical or middle or the center somehow of these numbers and as we'll see there's many types of averages the first is the one that you're probably most familiar with it's the one when people talk about hey the average on this exam or the average height and that's the arithmetic mean so let me write it in I'll write it in yellow Aerith arithmetic arithmetic mean when arithmetic is a noun we call it arithmetic when it's an adjective like this we call it arithmetic arithmetic mean and this is this is really just the sum of all the numbers divided by and this is a human constructed definition that we've found useful the sum of all of these numbers defined divided by the number of numbers we have so given that what is the arithmetic mean of this data set well let's just compute it it's going to be four plus three plus one plus six plus one plus seven over over the number of data points we have so we have six data points so we're going to divide by six and we get 4 plus 3 is 7 plus 1 is 8 plus 6 is 14 plus 1 is 15 plus 7 15 plus 7 is 22 we do that one more time you have 7 8 14 15 22 all of that over 6 and we could write this as a mixed number 6 goes into 22 three times with the remainder of 4 so it's 3 + 4 6 was the same thing as 3 + 2 2/3 we could write this as a decimal with 3.6 repeating so this is also 3.6 repeating we could write at any one of those ways but this is kind of a representative number this is trying to get at a central tendency once again these are human constructed no one ever it's not like someone just found some you know religious document that said this is the way that the arithmetic mean must be defined it's not as pure of a of a computation as say finding the circumference of the circle which there really is that was kind of we studied the universe and that just fell out of our study of the universe it's a human constructed definition that we found useful now there are other ways to measure the average or find a typical or middle value the other very typical way is the median and I will write median I'm running out of colors I will write meeting in pink so there is the median and the median is literally looking for the middle number so if you were order all the numbers in your set and find the middle one then that is your median so given that what's the median of this set of numbers going to be let's try to figure it out let's try to order it so we have one then we have another one then we have a three then we have a four a six and a seven so all I did is I reorder this and so what's the middle number well you look here since we have an even number of numbers we have six numbers there's no there's not one middle number you actually have two middle numbers here you have two middle numbers right over here you have the three and the four and in this case when you have two middle numbers you actually take you actually go halfway between these two numbers or essentially you're taking the arithmetic mean of these two numbers to find the median so the median is going to be halfway in between three and four which is going to be three point five so the median in this case the median in this case is three point five so if you have an even number of numbers the median over the middle to the essentially the arithmetic mean of the middle two or halfway between the middle two if you have an odd number of numbers it's a little bit easier to compute and just so that we see that let me give you another data set let's say our data set I'll order it for us let's say our data set was 0 750 I don't know 10,000 10,000 and 1 million 1 million let's say that that is our data set kind of a crazy data set but in this situation what is our median well here we have five numbers we have an odd number of numbers so it's easier to pick out a middle the middle is the number that is that is greater than two of the numbers and is less than two of the numbers it's exactly in the middle so in this case our median is 50 now the third measure of central tendency and this is the one that's probably used least often in life is the mode and people often forget about it and it sounds like something very complex but what we'll see is it's actually a very straightforward idea and in some ways it is the most basic idea so the mode is actually the most common number in a data set if there is a most common number if all the numbers are represented equally if there's no one single most common number then you have no mode but what given that definition of the mode what is the single most common number in our original data set in this data set right over here well we have only have one four we only have one three but we have two ones we have one six and one seven so the number that shows up the most number of times here is is our one so the mode the most typical number the most common number here is is a one so you see these are all different ways of trying to get at a typical or middle or central tendency but they you do it in very very different ways and as we study more and more statistics we'll see that they're good for different things this is used very frequently the median is really good if you have some kind of crazy number out here that could have otherwise skewed the arithmetic mean the mode could also be useful in situations like that especially if you do have one number that's showing up a lot more frequently anyway I'll leave you there and we'll the next few videos we will explore statistics Eve and Eber