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Stem-and-Leaf Plots

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Hi, this tutorial covers a type of graph called the Stem-and-Leaf Plot. So let's start with some data. The following data shows the number of calories for 10 different, six-inch Subway sandwiches. So notice the 450 here. That means there are 450 calories in the first sandwich, 490 calories in the second sandwich, et cetera. So, when quantitative data sets are small, a stem-and-leaf plot can be used to display the data.

So it's always nice to graphically display the data, and the best way to-- good way of graphing this type of data is with a stem-and-leaf plot. So let's get an example of a definition of what a stem-and-leaf plot. So stem-and-leaf plot, or just a stemplot, is a type of graph where quantitative data-- OK, so does need to be quantitative data is rounded to two significant digits then grouped into intervals

You will be working with rounded data here, and it does need to be to two significant digits. The intervals are the stems. And the individual data values are the leaves. OK, now a key must always accompany a stem-and-leaf plot. So that key is going to be really important.

All right, so let's try to make a little bit of sense now of this definition. All right, so I'm going to make the stem-and-leaf plot on this page here, and I've included the data above. All right so, what's nice about this data set is, Subway already rounded these values to two significant digits when they reported it.

So maybe this sandwich actually had 452 calories. OK, like this rounds down to 450. So we can just have two digits here. And then the last one just being 0. OK, If we had numbers with four digits, OK, again, we'd only want the first two digits to be values other than 0.

OK, so what we're going to do now is we're going to let the largest-place value be the stems plate, the numbers on the stem. So all of these numbers are in the hundreds. So we're going to put 100s in the stem. OK, so what I'm going to do is I'm going to make a stem. And generally I make it using two vertical bars.

So now what I do is I look for the smallest value. So the smallest value is 210. So the number in the 100s place for the smallest value is two. So that's how I'm going to start my stem. OK, now I need to look for the biggest value. So the biggest value is 630. So I need to go count from two to six.

OK, make sure you don't skip any values, and try to keep your values kind of similar spacing. I could include seven here if I'd like. Now you can always go a little bit further or start a little bit less than your smaller value.

OK, now what I'm going to do is I'm going to start identifying data values using what are called leaves. So the leaves are going to grow out of the stem this way. All right, so I'm going to start with my smallest value, which is 210, OK. The way I'm going to represent that is by putting a one right here. So that represents the tens place. So this means it has two in the hundreds, one in the tens, and then since it's rounded, we're always going to assume there's a zero in the ones.

OK, now that the leaves always have to go on in order. So now I'm need to find the next smallest value. And that's 280. So what I'm going to do here now is just put an eight next to the one. OK, so that represents 280. So, so far we have 210, 280 displayed. OK, now my next one is 290. So I'm going to place a nine here like so, and I think that takes care of all of the 200s. It does.

OK, so now we go to 300. So we have two values in the 300s. So we have 360 and 390. OK, now into the 400s, so we have 410. Now we have two 450s, so we need to make sure that we get two fives on here. OK, and now notice I'm lining up the numbers, and I'm trying to make the numbers about the same width. So that, if this has three values and this has three values, they both end at the same spot.

OK, but I do have one more 400, so I'm going to do 490 there. OK, and I don't have any 500s, but it's still important that you leave space there. So we make sure to include the five in the stem, even though we don't have it, and then 630 is that way.

OK, now what I said before is that a key must always accompany a stem-and-leaf plot, OK. The reason that's important is that stem-and-leaf plot are pretty versatile. Instead of this representing 210 this could also represent 21. It could even represent 2.1 or even 2,100. So it's important that, down here in your key, you just give an example. So I would say three, if three is in the stem, six is a leaf, this would represent 360. OK, so that would represent-- this would be now a stem-and-leaf plot for the calorie data for Subway.

All right, another type of stem-and-leaf plot that is commonly used is what's called a back to back stem-and-leaf plot. Sometimes it's also called a comparative stem-and-leaf plot. And it's a type of stem-and-leaf plot where two similar data sets can be compared. So now if we look at another sandwich place, McDonald's, common fast food restaurant, now we also had 10 McDonald's sandwiches.

Now your data sets don't necessarily need to be the same size. OK, they are in this case. So we have 600, 430, 540, et cetera. So now let's go ahead and use the same stem-and-leaf plot for Subway, but now let's also put the McDonald's data on here. So I'll get the McDonald's data, so we can see that also. I'll just have to leave that up. So what we'll do is find the smallest McDonald's data value. So the smallest one here was 280.

So what we're going to do is we're going to let this side represent Subway, and we're going to let this side now represent McDonald's. OK, so, since 280 was the smallest, we're going to put an eight going this way. OK, so this might look like 820, but remember, this still represents the 100s place. So this actually represents 280. OK, so now my next-- I don't have any other in the 200s. So the next one is one in the 300s. It was 330. So we're going to put a three here. So that represents 330.

OK the 400s, we had 430 and 490. So we put a three here and a nine here. Now they're going in order, going from least to greatest as they leave the stem. So they're going least to greatest this way but least to greatest this way for McDonald's. OK, 500, there were four values, 510, 540, 540, and 590. OK, so again, trying to keep my numbers about the same size.

OK, now we look at 600, 600 we represent this way as six in the hundreds place zero in the tens place. And then I also had one that was in the 700s, . 770 OK, so I'm going to use this seven that I had before. If not, I could have created it there. So this is what's called a back-to-back stem-and-leaf plot.

Now what's nice about this is you can easily now compare these two samples. OK, we can see that it looks like McDonald's sandwiches, because there's more values in the upper range here, generally seems to have more calories than a Subway sandwich. We can see here, most of the Subway sandwiches, or a lot of the Subway sandwiches, are in the 400s in terms of calories. A lot of the sandwich from McDonald's are in the 500s in terms of calories.

Then a lot of times also, if you're using a back-to-back stem-and-leaf plot, you might want to also put another stem just to say now that that represents 430 on the other side. So that has been the tutorial on stem-and-leaf plots. Thanks for watching.