Stem and Leaf Chart
This sort of chart is used to put numbers in order of size.
It also gives an idea of the ‘distribution’ (like a histogram).
Example:
Put these numbers into order:
123, 135, 107, 113, 145, 147, 132, 144, 156, 143, 121, 145, 151, 159, 100, 107
First draw out an “unordered” stem-and-leaf. These are just the numbers from the list above.
10
11
12
13
14
15
7
3
3
5
5
6
0
7
1
2
7
1
4
9
3
5
Then rewrite the table with the numbers in order:
10
11
12
13
14
15
0
3
1
2
3
1
7
7
3
5
4
6
5
9
5
7
Then copy out the list from the ordered table:
100, 107, 107, 113, 121, 123, 132, 135, 143, 144, 145, 145, 147, 151, 156, 159
You can also see the ‘distribution’ (shape) of the data:
10
11
12
13
14
15
0
3
1
2
3
1
7
3
5
4
6
Two questions:
7
Use stem-and leaf diagrams to put these lists in
order:
5
9
5
7
There is a peak in the data (lots of numbers) in the 140s.
You’ll learn more about describing distributions later.
1. 108, 119, 119, 124, 144, 138, 126, 145, 155,
138, 137, 134, 137, 121
2. 21, 35, 44, 21, 27, 36, 46, 41, 60, 29, 29, 45,
38, 44, 61
5 Number Summary
These are the numbers needed to draw a chart called a boxplot.
You need a list of data in order to work them out.
They are min (minimum), LQ (Lower Quartile), med (median), UQ (upper quartile) and max (maximum)
Example:
The min is easy (smallest) = 100
The max is easy (biggest) = 159
100, 107, 107, 113, 121, 123, 132, 135, 143, 144, 145, 145, 147, 151, 156, 159
Start by crossing off numbers from either end of the list (ie the smallest and the biggest number each time).
100, 107, 107, 113, 121, 123, 132, 135, 143, 144, 145, 145, 147, 151, 156, 159
Keep going until you reach the middle
100, 107, 107, 113, 121, 123, 132, 135, 143, 144, 145, 145, 147, 151, 156, 159
If there is a middle number, that is the median.
Sometimes there are two middle numbers.
Find their average: (135 + 143) ÷ 2 = 139
To find the lower quartile and upper quartile, you do the same with the bottom and top halves of the list:
100, 107, 107, 113, 121, 123, 132, 135, 143, 144, 145, 145, 147, 151, 156, 159
So the LQ is between 113 and 121 = (113 + 121) ÷ 2 = 117
So the UQ is between 113 and 121 = (145 + 147) ÷ 2 = 146
Finished:
Min
LQ
Med
UQ
Max
100
117
139
146
159
Two questions:
Find the 5 number summary for these two lists. They are already in order:
1. 108, 119, 119, 121, 124, 126, 134, 137, 137, 138, 144, 145, 155
2. 21, 21, 27, 29, 29, 35, 36, 38, 41, 44, 44, 45, 46, 60, 61
Box Plots
Used to compare two sets of data. They use a ‘5 Number Summary.’ (Min – smallest number, LQ – Lower Quartile,
Med – Middle Number, UQ – Upper Quartile, Max – biggest number).
Example:
Draw a boxplot for this 5 point summary:
Min
LQ
Med
UQ
Max
100
117
139
146
159
First draw a scale. It needs to go AT LEAST from min to max.
100
110
120
140
150
160
130
140
150
160
130
140
150
160
130
Then draw in a line for each of the 5 numbers:
100
110
120
Complete the boxes and whiskers:
100
110
120
Two questions:
Draw boxplots for these 2 5-number summaries:
Min
LQ
Med
UQ
Max
108
121
134
138
155
Min
LQ
Med
UQ
Max
21
29
38
44.5
61
Histograms
Used to look at the ‘shape’ of the data.
Example:
Draw a histogram for this data:
123, 135, 107, 113, 145, 147, 132, 144, 156, 143, 121, 145, 151, 159, 100, 107
It needs grouping. This is sometimes hard!
Tally
100-110
110-120
120-130
130-140
140-150
150-160
Frequency
3
1
2
2
5
3
Then graph:
THE LABELS ARE AT THE SIDES OF THE BARS.
You can then draw an outline to describe the distribution
(‘shape’) of the data.
Two questions:
Draw histograms for these sets of data:
1. 108, 119, 119, 124, 144, 138, 126, 145, 155,
138, 137, 134, 137, 121
2. 21, 35, 44, 21, 27, 36, 46, 41, 60, 29, 29, 45,
38, 44, 61
Checking Example
Make sure that everyone in your group can:
1.
2.
3.
4.
Draw a stem-and-leaf chart
Calculate a 5 number summary
Draw a boxplot
Draw a histogram
Do each of these (in this order) for this data, explaining your area of expertise as you go:
These are the heights of some girls in year 9:
143, 157, 143, 169, 168, 155, 142, 159, 170, 140, 145, 159
Then each of you try this set of heights:
148, 159, 149, 173, 172, 175, 142, 164, 165, 140, 142, 150