stem and leaf diagrams sometimes called ‘stem and leaves’ too

Stem and leaf diagrams

Sometimes called ‘stem and leaves’ too

They really are as simple as they seem

Simply a way of showing the values of data

Example……..

Here are the weights of some aardvarks (kg):

12, 28, 17, 17, 19, 23, 9, 7, 25, 34, 21

Stem and leaf might look like this:

Weight of aardvarks

0 9, 71 2, 7, 7, 9, 2 8, 3, 5, 1 KEY3 4 1 2 is 12kg

STEM LEAF OR LEAVES

Don’t need to write this usually

Your ‘stem and leaf’ must have a…

1. Title

2. Key – so that other people can work out what your values are.

An ordered ‘stem and leaf’….

Has the values in size order.

So for our example before…

Weight of aardvarks

0 9, 7

1 2, 7, 7, 9,

2 8, 3, 5, 1 KEY

3 4 1 2 is 12kg

The ordered ‘stem and leaf’ would be:

Weight of aardvarks

0 7, 9

1 2, 7, 7, 9,

2 1, 3, 5, 8 KEY

3 4 1 2 is 12kgWhat weight does the ‘5’represent?

Show the following data as a stem and leaf diagram

I.Q. scores of Year 10 girls:

105, 98, 112, 94, 130, 121, 98, 104, 100, 108, 112, 104, 101, 97, 104

I.Q. scores of Year 10 girls

9 8, 4, 8, 7

10 5, 4, 0, 8, 4, 1, 4

11 2, 2

12 1

13 0

KEY 11 2 means 112

Now ‘order it’

I.Q. scores of Year 10 girls(unordered)

9 8, 4, 8, 7 10 5, 4, 0, 8, 4, 1, 4 11 2, 2 12 1 13 0 KEY 11 2 means 112

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

The ordered one can be used to find lots of information

Mode….

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

Mode – most common

In this case 104

Range ….

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

Highest value – lowest value

In this case:

Range = 130 – 94 = 36

Median ….

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

1. Put in size order (already done);

2. then find the middle value

In this case we have 15 values so we want the

median = 104

8th value along

Lower Quartile ….

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

1. Put in size order (already done);

2. then find the value a quarter of the way up

In this case we have 15 values so we want the

Lower quartile = 98

4th value along

Upper Quartile ….

I.Q. scores of Year 10 girls (ordered)

9 4, 7, 8, 8 10 0, 1, 4, 4, 4, 5, 8 11 2, 2 12 1 13 0 KEY 11 2 means 112

1. Put in size order (already done);

2. then find the value three- quarters of the way up

In this case we have 15 values so we want the

Upper quartile = 112

12th value along

You now know enough to be able to draw a ‘box and whisker diagram’

Smallest value Largest value

median

Lower quartile upper quartile

90 100 110 120 130 I.Q. Score

Now for the boys……..

Show the following data as a stem and leaf diagram

I.Q. scores of Year 10 boys:

103, 98, 112, 99, 108, 122, 98, 104, 100, 108, 112, 104, 101, 97, 104, 108, 99, 108, 102

I.Q. scores of Year 10 boys

9 8, 9, 8, 7, 9

10 3,8,4,0,8,4,1,4,8,8,2

11 2, 2

12 2

KEY 11 2 means 112

Now ‘order it’

I.Q. scores of Year 10 boys

(unordered)

9 8, 9, 8, 7, 9

10 3,8,4,0,8,4,1,4,8,8,2

11 2, 2

12 2

KEY 11 2 means 112

I.Q. scores of Year 10 boys

(ordered)

9 7, 8, 8, 9, 9

10 0,1,2,3,4,4,4,8,8,8,8

11 2, 2

12 2

KEY 11 2 means 112

Mode ……

I.Q. scores of Year 10 boys

9 7, 8, 8, 9, 9

10 0,1,2,3,4,4,4,8,8,8,8

11 2, 2

12 2

KEY 11 2 means 112

Mode – most common

In this case 108

Range ……

I.Q. scores of Year 10 boys

9 7, 8, 8, 9, 9

10 0,1,2,3,4,4,4,8,8,8,8

11 2, 2

12 2

KEY 11 2 means 112

Highest value – lowest value

In this case:

Range = 122 – 97

= 25

Median ……

I.Q. scores of Year 10 boys

9 7, 8, 8, 9, 9

10 0,1,2,3,4,4,4,8,8,8,8

11 2, 2

12 2

KEY 11 2 means 112

1. Put in size order (already done);

2. then find the middle value

In this case we have 19 values so we want the

median = 104

10th value

Lower Quartile ……

I.Q. scores of Year 10 boys

9 7, 8, 8, 9, 910 0,1,2,3,4,4,4,8,8,8,811 2, 212 2

KEY 11 2 means 112

1. Put in size order (already done);

2. then find the value a quarter of the way up

In this case we have 19 values so we want the

Lower quartile = 99

5th value

Upper Quartile ……

I.Q. scores of Year 10 boys

9 7, 8, 8, 9, 910 0,1,2,3,4,4,4,8,8,8,811 2, 212 2

KEY 11 2 means 112

1. Put in size order (already done);

2. then find the value three- quarters of the way up

In this case we have 19 values so we want the

Upper quartile = 108

15th value

Now draw a box and whisker diagram to compare the I.Q. of boys and girls

you can draw this one on the same diagram as before.

Here we go …..

90 100 110 120 130 I.Q. Score

GIRLS

BOYS

What can you say about boys and girls I.Q.s ?