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