how to make a stem and leaf plot

When you compare them to histograms or boxplots, stemplots (or stalk and leafage plots) are much more simple and straightforward to not only put together only also to read. This, along with the fact that you don't lose information about private data values is ane of the benefits of a stemplot. The only existent downside to selecting a stemplot to represent your information prepare is that it can be overly complex for large information sets and await kind of goofy if the range of your data set is small (I'll explicate this after we run into how to make one).

So let'south apply the following small, made-up data set to see how to make a stemplot.

half-dozen	12	4	xiv	35	33	35	37	xviii	42
45	38	34	34	42	51	58	50	68	72

Pace ane: Pick your "stems" and "leaves"

Each of the numbers in your data set can be viewed as being made up of two parts: a stalk and a leaf. You want to pick it so that the leaf volition exist 1 digit (the reason for this will make sense in a minute). For this information ready, the tens digit will be the stem and the ones digit will be the foliage.

stem and leaf

For single digit numbers, we volition use a naught as a placeholder for the tens digit. The picture below shows how we will think about this for the showtime information value of 6.

stem and leaf 2

Footstep ii: Describe a vertical bar with all of the stems on the left

This footstep sounds much more complicated than it actually is. Nosotros want to look at our data gear up and figure out the smallest and the largest stems. Nosotros will count upwards without skipping any numbers at all. For this data set:

Smallest value: 6 (so the smallest stem is 0)
Largest value: 72 (so the largest stem is 7)

And then on the left of our bar we will write out all the whole numbers from 0 to 7.

stems

That's manner easier once y'all actually encounter it right? Find that even though we don't take any data values in the 20s that I still put a 2 there. You lot shouldn't skip any values!

Footstep 3: Put each leaf next to its stem, in guild

For this step, it might be helpful to put your information gear up in order from smallest to largest. Hither is our original data set.

half-dozen	12	4	fourteen	35	33	35	37	xviii	42
45	38	34	34	42	51	58	50	68	72

Hither is the aforementioned information gear up in order from smallest to largest.

4	6	12	14	eighteen	33	34	34	35	35
37	38	42	42	45	l	51	58	68	72

You tin can do this all at in one case, just just to make sure you see where all the numbers are coming from, permit'southward do information technology in a couple of steps. Showtime, permit'southward put the 4 and 6 on the plot.

stemplot-1

Now yous come across what I hateful by "put the value side by side to its stalk in guild". Now to finish this, we will proceed the same process. Since there are no values with a stem of ii, we just skip that. Also, whenever in that location are repeats, nosotros volition just list the foliage function twice. So you lot don't accept to scroll, hither is the finished stemplot forth with the data set.

iv	half-dozen	12	14	18	33	34	34	35	35
37	38	42	42	45	50	51	58	68	72

stemplot-finished

Also, find that we added a title (though here this is made up data, and so it is a boring title!) and a key. Every stemplot should have a key because it could be that the data values are decimals and a stalk of 3 and a leafage of 4 represents 3.iv and not 34! Without a key, how would we know?

Finally, equally I mentioned, for some data sets a stemplot might not exist as useful. You can probably imagine that if there were 1000 information values that this would be tough to read and seem busy. But likewise, imagine if all of the values had the same stem! What if your data fix was 100, 108, 109, 109, 109, 108, 107, 106, 104… well you lot go the idea…? Then your stemplot wouldn't be much meliorate than a list of numbers. There are ways around this (breaking upward the stem into 2 or three parts) but in the terminate, information technology might be better to apply something similar a dotplot for a data ready like this.