Stemplot Lecture

8/4/2019 Stemplot Lecture

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Stemplot lecture from Chapter 1

Stemplots are used to approximate Histograms, particularly when all we need is an id

Below are some examples of stemplots.

Example 1

Data Sorted Data The first step is optional but helpful; put the data i

17 12

13 13 Second, separate the “stems” from the “leaves”.

16 13

19 16 The “leaf” is the rightmost digit* in the number.

12 17 The “stem” is all the digits that are left after the lea

13 19 So for the number 12, 2 is the leaf, and 1 is the st

26 21

21 24 The third step is to write the stems in a vertical col

24 26 horizontal row next to their respective stem.

28 28* Recall: there are 10 digits: 0,1,2,3,...,9. Number

Stems Leaves

1 233679 We interpret the stemplot as a histogram turned o

2 1468 and the 2 stem is on the right. The shape of this d

roughly symmetric – its hard to say because the d

considered correct.)

Example 2

Data Sorted Data Modified Data If the data have decimals, ignore

0.17 0.12 12 So treat 0.17 as 17, 0.13 as 13, e0.13 0.12 12 data, but that's o.k. A stemplot is

0.16 0.13 13 position of the data values to eac

0.19 0.16 16 data the same way, this relative p

0.12 0.17 17 ignoring the decimals is the same

0.12 0.19 19

0.26 0.21 21 Note that the Modified Data is the

0.21 0.24 24 Therefore the stemplot will be the

0.24 0.26 26

0.28 0.28 28 Stemplot:

1 223679

2 1468

Example 3

Sorted Data In this case, what do we do with single digit numbers, like 2? We

2 We normally don't do that, but if we wanted to we could write 2 as

3 It means zero tens and two ones. 2 means two ones, which is th

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3 to, we could write 2 as 002 or 0002, etc. 002 means zero hundre

7 The idea is we want all the stems to have the same number of dig

9 So 2 becomes 02, 3 becomes 03, etc., and the leaf for 02 is 2, th

9

11 The stemplot looks like:

11

11 0 23379911 1 111122255566

12 2 1122233667

12

12 Its a bit hard to see the shape since the rows are pretty long – the

15 When that happens, we can “split the stems” to get a better idea

15 To split the stems, write each stem twice, like this

15

16 0

16 0

21 1

21 1

22 222 2

22

23 Then we put the leaves 0 through 4 on the top stem, 5 through 9

23 So the stemplot with split stems looks like this:

26

26 0 233 (top stem)

27 0 799 (bottom stem)

1 1111222 (top stem)

1 55566 (bottom stem)

2 1122233 (top stem)

2 667 (bottom stem)

From this split-stem stemplot we can see that the distribution is sli

right is down on a stemplot). Since the skew is very slight, you co

symmetric (sort of a glass half full or half empty kind of thing).

Example 4

Sorted Data

78 Since we've got two digit numbers and 3 digit numbers, we're goi

95 So 78 will become 078, 95 will become 095, etc. Our stems will t

96 The first few stems will be 07, 09, 10, 11, etc. Notice that we don'

103 In fact, there are lots of “missing stems” - there's no 16, 18, or 19,

112 Its very important that we include these missing stems in our stem134 They are like bins in a histogram with no data in them (no bars in

141 on the shape of the distribution so we must include them. Reme

145 mistake in making stemplots. The odds are very high that someo

147 Will it be you?? Say it 'aint so!

148

153 Notice that with the “missing stems” included in the stemplot, it is

158

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172 Stemplot: (ignore the decimals in the first three stems; I had

172

200 .07 8

255 .08 We can see that the data is really

271 .09 56 tell what the shape is. When the

359 10 3 we split the stems. When its too

11 2 Again this is changing the values,12 of the values in the stemplot stay

13 4

14 1578 When we round data, we chop off

15 38 Notice that every number will end

16 getting too technical, those zeros

17 22 so we chuck them. Then we red

18

19 In this case we will round to the n

20 0 accuracy to the ones place. So 7

21

22 Rounded Data Zeros removed

2324 80 8

25 5 100 10

26 100 10

27 1 100 10

28 110 11

29 130 13

30 140 14

31 150 15

32 150 15

33 150 15

34 150 15

35 9 160 16170 17

170 17

200 20

260 26

270 27

360 36

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ea of the shape of a distribution.

numerical order.

f is removed.

m. For 13, 3 is the leaf, 1 is the stem, etc.

umn, and the leaves for each stem in a

s are made up of digits; e.g. 527 has the digits 5, 2, and 7.

n its side, in this case so the 1 stem is on the left

istribution would be slightly skewed right, or

ta set is so small. (Either answer would be

them and any leading zeros.

tc. This changes the value of thea graph that shows the relative

other – as long as we change all the

osition is preserved. E.g., in this case

as multiplying all the data by 100.

same as the Sorted Data in Ex. 1.

same.

write them as two digit numbers.

02. What does 02 mean?

same thing. If we wanted

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s, zero tens, and two ones.

its, in this case one digit each.

stem is 0.

data is bunched up.

f the shape.

n the bottom stem.

ightly skewed left (remember left is up,

uld also say this is roughly

g to write all of them with three digits.

erefore have two digits.

't have any data with a stem of 08.

for example.

plot, since they act as placeholders.those bins). They have an effect

ber this! It is the most common

ne will make this mistake on an exam.

very loooooong.

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to put them in to get a leading zero.)

spread out – too spread out to

data was too bunched together

spread out, we round the data.

but that's ok since the relative positionsthe same.

and discard the rightmost zeros.

in zero when we round; without

don't contain any useful info

the stemplot with the rounded data.

earest ten, since our data started with

8 becomes 80, 95 becomes 100, etc.

Now we can see that our stems willbe 0, 1, 2, and 3 – a lot fewer than

before

The new, rounded-data stemplot:

(again, ignore the decimal; had to put it in to get leading zeros)

0 8

1 .0001345555677

2 .067

3 6

This new stemplot is a little too bunched up.It would be moreso if drawn by hand. So

let's split the stems.

Rounded, stem-split stemplot:

0

0 8

1 .000134

1 5555677

2 0

2 67

3

3 6

This last one is easier to read – i.e. its

easier to tell the shape of the distribution,

which in this case is skewed right.

Note that if the very top (or very bottom) stem

has no leaves, you can leave it off, like

this:

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0 8

1 .000134

1 5555677

2 0

2 67

33 6

Notice there is only one 0 stem,

since the lower one had no leaves.

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