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# Stem and Leaf Plots

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- In this video, we're going to talk about how
- to visualize data.
- In particular, we're going to use something called a stem
- and leaf plot.
- And what's useful about this is it essentially allows you
- to show all of your data and show a lot of detail about all
- of the numbers in your data set, while at the same time
- having a good sense about how those numbers in your set are
- distributed.
- Right here, I have a set of numbers.
- And when I just look at this, it really doesn't make a lot
- of sense to me.
- It's just a bunch of numbers to me.
- I have no sense are more of them closer to 20 or 30?
- Are more of them closer to 80?
- Is their median or their mode 30 or 40 or 84?
- I have no idea, just looking at this list of numbers.
- But using a stem and leaf plot, hopefully, some of this
- will become a little bit more apparent.
- And the idea here is to list the most significant digit in
- each of those numbers in the stem.
- So when we talk about the most significant digit, these
- numbers right here, they range-- let's
- see, we have a 2 here.
- That looks like-- we have a 1.
- That looks like our lowest number.
- And it goes all the way up to 84.
- It has a bunch of numbers in between in the teens, in the
- twenties, in the thirties, forties, fifties, sixties.
- so on and so forth.
- So it looks like the most significant digit here is the
- tens digit.
- So let's write it right here.
- Let's write our tens digit.
- And the tens digit could be a 0, 1, 2, 3, 4-- let me write
- this a little bit bigger.
- 0, 1, 2, 3, 4, 5, 6, 7 or-- let me scroll down a little
- bit-- an 8.
- These digits will represent our stem.
- So I'm going to draw this little line around here.
- This is going to be a our stem right there in the
- stem and leaf plot.
- For a number like 1, the tens digit is 0.
- You could imagine it as 01.
- For a number like 84, the tens digit is obviously 8.
- So what I'm going to do is rewrite all of these numbers
- here using the stem and leaf plot.
- And the technique here, and I'm just going to show you by
- example, let's go through each of these numbers.
- Let's say I want to write 35.
- So 35-- let me cross it out.
- 35, so it has a tens digit of 3.
- I'll put a 5 right here.
- That tells me that 35 is one of my numbers.
- Then I have 42.
- Cross it out, let me know I used it.
- 42, I'm writing the ones digit as leaves.
- You're going to see what I'm going to do.
- Let's see.
- 38.
- Well, I have a 30.
- I'm going to write an 8 here.
- So I didn't have to rewrite the 30.
- I'm just saying, look, I have a 35 and I have a 38.
- I'm just writing the ones digits within the three stem,
- within the tens place, within the thirties place, however
- you want view it, the thirties bucket.
- Then we have a 57.
- We have a 2, which you could just view as 02.
- We have a 2.
- We have 24, 27, 36.
- We have a 35, a 38, and a 36, 45, 60.
- I think you get the idea, but just for the sake of
- completion, let's finish all of these.
- 38, 40, another 40, a 44, a 1, another 44, a 48-- there's a
- lot of things in this forties bucket-- 48, an 84, a 38, a
- 20, a 4-- put that right there, 04-- a 2.
- It's getting a little monotonous, but
- let's just finish it.
- 48, another 48 right there, a 58, a 3.
- Stick it up there.
- It's 03.
- Then we have a 20, a 6, a 40, 22, 26, 17.
- That's our first number in the teens bucket.
- An 18, a 40-- a lot of things in the forties-- a 51, 62, 31,
- 27, 48, 35-- almost done-- 27, 37, 58 and 21.
- And we have our 21.
- And just like that, it was a little monotonous, but we
- essentially just rewrote this list of numbers down here.
- I have every number represented.
- We haven't lost any information here.
- I know every number.
- I could go start with this, and I could tell you every
- number that I had in my original list. I have a 6, I
- have a 27, I have a 38, a 35.
- So we haven't lost any information.
- But what's neater about this representation is when the
- numbers are written this way, we actually save ink, because
- you don't have to rewrite the 40 to 45.
- You just write the ones digit.
- But more importantly, we kind of understand how the numbers
- are distributed, that we have a bunch of numbers in the
- forties and thirties and twenties.
- That's where most of the numbers are.
- We have very few numbers up in the eighties.
- We have no numbers in the seventies.
- We have very few.
- We have a lot in the ones, but still, most of them are
- focused in this range over here.
- So this is just one of many, many, many ways to visualize
- data that you will run into in your mathematical or
- statistical futures.
- But I just wanted to expose you to this.

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