Stem and Leaf Diagrams © Christine Crisp “Teach A Level Maths” Statistics 1.

Stem and Leaf Stem and Leaf DiagramsDiagrams

© Christine Crisp

““Teach A Level Teach A Level Maths”Maths”

Statistics 1Statistics 1

Stem and Leaf Diagrams

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Statistics 1

AQA

EDEXCELMEI/OCR

OCR


You met some statistical diagrams when you did GCSE.

The next three presentations and this one remind you of them and point out some details that you may not have met before.

We will start with stem and leaf diagrams ( including back-to-back ).

Stem and leaf diagrams are sometimes called stem plots.


Weekly hours of 30 men

5

4

4

3

3

2

2

5 1

4 5 6

4 1 1 2

3 5 5 5 5 5 5 6 6

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

2 8

2 1

e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men 35 41 33 31 30 45 35 36 51 32

32 30 28 35 34 33 35 36 32 42

33 31 41 21 34 35 34 46 32 35

The stem shows the tens . . .

I’ll use intervals of 5 hours to draw the diagram i.e. 20-25, 26-30 etc.

and the leaves the units

e.g. 46 is 4 tens and 6 units



e.g. The table below gives the number of hours worked in a particular week by a sample of 30 men

5 1

4 5 6

4 1 1 2

3 5 5 5 5 5 5 6 6

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

2 8

2 1


35 41 33 31 30 45 35 36 51 32

32 30 28 35 34 33 35 36 32 42

33 31 41 21 34 35 34 46 32 35


Weekly hours of 30 menThe stem shows the

tens . . . and the leaves the units




5 1

4 5 6

4 1 1 2

3 5 5 5 5 5 5 6 6

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

2 8

2 1


35 41 33 31 30 45 35 36 51 32

32 30 28 35 34 33 35 36 32 42

33 31 41 21 34 35 34 46 32 35



N.B. 35 goes here . . . not in the line below.

The stem shows the tens . . . and the leaves the units



5 1

4 5 6

4 1 1 2

3 5 5 5 5 5 5 6 6

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

2 8

2 1


35 41 33 31 30 45 35 36 51 32

32 30 28 35 34 33 35 36 32 42

33 31 41 21 34 35 34 46 32 35

e.g. 46 is 4 tens and 6 unitsWe must show a key.

Key: 3 5 means 35 hours

Weekly hours of 30 menThe stem shows the

tens . . . and the leaves the units


5 1

4 5 6

4 1 1 2

3 5 5 5 5 5 5 6 6

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

2 8

2 1


If you tip your head to the right and look at the diagram you can see it is just a bar chart with more detail.Points to

notice:• The leaves are in numerical order• The diagram uses raw ( not grouped )

data



Finding the median and quartilesFinding these is easy because the data are in order.

Median: The median is the middle item, . . .

Tip: To find the middle use where

n is the number of items of data.2

1nso with 30 observations we need the th item, the average of 15 and 16.

515

12

82

444333222211003

665555553

2114

654

15 Weekly hours of 30 men



12

82

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665555553

2114

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15th

Median: The median is the middle item, . . . so with 30 observations we need the th item, the average of 15 and 16.

515



12

82

444333222211003

665555553

2114

654



15th

16th


515



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15th

16th

Since the 15th and 16th items are both 34, the median is 34.


515

( If the values are not the same we average them. )



12

82

444333222211003

665555553

2114

654



For the lower quartile (LQ) we first need 4

1n)757(

7th



12

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654



7th

8th


1n)757(



12

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7th

8th

The lower quartile is 32.


1n)757(



Finding the median and quartilesIf the values of the 7th and 8th observation are not the same, we interpolate to find the LQ.

and we want the 7·75th value, we need to add 0·75 of the gap between the 7th and 8th to the 7th value.

e.g. If we had7th value: 328th value: 36

So, The gap is 36 – 32 = 4.

0.75 of 4 is 3.

LQ = 32 + 3 = 35


12

82

444333222211003

665555553

2114

654


Finding the median and quartiles

)2523( For the upper quartile (UQ), we first need 4

)1(3 n

( or from the top end )757



12

82

444333222211003

665555553

2114

654



23rd


)1(3 n




12

82

444333222211003

665555553

2114

654



23rd

24th


)1(3 n




12

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444333222211003

665555553

2114

654



23rd

24th

The upper quartile is 36.The interquartile range (IQR) = UQ LQ

= 36 – 32 = 4


)1(3 n




12

82

444333222211003

665555553

2114

654



Stem and Leaf diagrams are used for small, raw data sets (not grouped data).

e.g.

The leaves are in numerical order ( away from the stem )

stem

leaves

The diagram must have a title and a key.

continued

SUMMARY


The median is the th piece of data.

2

1n

The quartiles are found at the th

position and the th position.

4

1n

4

)1(3 n

( If necessary, average 2 data

items )

The interquartile range (IQR) = UQ

LQ( upper quartile – lower

quartile ) If necessary, we can interpolate to find the

LQ and UQ.

Back-to-Back Stem and Leaf Diagrams

12

82

444333222211003

665555553

2114

654

15

Weekly hours Men

Key: 3 5 means 35 hrs

4 3

0

8 8 6 6 5 5 5 5

4 4 4 3 3 3 2 2 2

8

3 3 1 0

5 5 1

4 4 2 1

Back-to-back stem and leaf diagrams can be used to compare 2 sets of data relating to the same subject.In our example we could add the data for 30 women.

Women

Notice how easily we can compare the variability of the 2 data sets

Key: 5 3 means 35 hrs


456789

January Max Temperatures 1985 to 2005 Sheffiel

d

11625315794003489

1681258

2

Braemar

74

54320954

8422195421

0

Exercise

Find the medians and quartiles. What can you say about the temperatures of the 2 places?

Key: 3 4 means 3·4C



Answer:

The places have similar variability in temperature but Sheffield is about 2 ·7C warmer than Braemar.

Median

LQ UQ

Braemar 4·4 3·6 5·95

Sheffield

7·1 5·35 8·15

456789

January Max Temperatures 1985 to 2005 Sheffiel

d

11625315794003489

1681258

2

Braemar

74

54320954

8422195421

0



The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.



2

2

3

3

4

4

5

12

82

444333222211003

665555553

2114

654

15


This is used for small, raw data sets (not grouped data).

e.g.

The leaves are in numerical order ( away from the stem )

stem

leaves

The diagram must have a title and a key.

SUMMARY


The median is the th piece of data.

2

1n

The quartiles are found at the th

position and the th position.

4

1n

4

)1(3 n

( If necessary, average 2 data

items )

If necessary, we can interpolate to find the LQ and UQ.

The interquartile range (IQR) = UQ

LQ( upper quartile – lower

quartile )


12

82

444333222211003

665555553

2114

654

15


Weekly hours Men

1244

155

0133

8

222333444

55556688

0

34

Back-to-back stem and leaf diagrams can be used to compare 2 sets of data relating to the same subject.In our example we could add the data for 30 women.

Women


Notice how easily we can compare the variability of the 2 data sets

Stem and Leaf Diagrams © Christine Crisp “Teach A Level Maths” Statistics 1.

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Transcript of Stem and Leaf Diagrams © Christine Crisp “Teach A Level Maths” Statistics 1.