Transcript “Teach A Level Maths” Statistics 1 Cumulative Frequency Diagrams © Christine Crisp A stem and leaf diagram is used to show simple raw data which can.

“Teach A Level Maths”
Statistics 1
Cumulative Frequency
Diagrams
© Christine Crisp
A stem and leaf diagram is used to show simple raw data
which can be written out as a list of values.
In most cases, however, data will have been grouped into
classes and a frequency given for each class.
Grouped frequency data can be displayed in a cumulative
frequency diagram.
e.g. The projected population of the U.K. for 2005, by age:
AGE
Freq
Cu.F
( years )
(millions)
(millions)
0–9
7
7
10 – 19
8
15
20 – 29
7
22
30 – 39
9
31
40 – 49
9
40
50 – 59
8
48
60 – 69
6
54
70 – 79
4
58
80 – 89
2
60
90+
0
60
Source: USA IDB
Why does this appear as 0?
ANS: The data are given to
the nearest million. The
projected figure was 113,000.
In drawing the diagram I
shall miss out this group.
e.g. The projected population of the U.K. for 2005, by age:
AGE
Freq
Cu.F
( years )
(millions)
(millions)
0–9
7
7
10 – 19
8
15
20 – 29
7
22
30 – 39
9
31
40 – 49
9
40
50 – 59
8
48
60 – 69
6
54
70 – 79
4
58
80 – 89
2
60
Source: USA IDB
Points to notice:
• There is no gap between 9
and 10 as the data are
continuous.
• Points are plotted at upper
class boundaries (u.c.bs.)
e.g. the u.c.b. for 0 - 9
would normally be 9·5
e.g. The projected population of the U.K. for 2005, by age:
AGE
Freq
Cu.F
( years )
(millions)
(millions)
0–9
7
7
10 – 19
8
15
20 – 29
7
22
30 – 39
9
31
40 – 49
9
40
50 – 59
8
48
60 – 69
6
54
70 – 79
4
58
80 – 89
2
60
Points to notice:
• There is no gap between 9
and 10 as the data are
continuous.
• Points are plotted at upper
class boundaries (u.c.bs.)
e.g. the u.c.b. for 0 - 9
would normally be 9·5
Age data have different u.c.bs.
Can you say why this is?
IDB
ANS: IfSource:
I askUSA
children
their ages, they reply 9 even if
they are nearly 10, so, the 0-9 group contains children
right up to age 10 NOT just nine and a half.
e.g. The projected population of the U.K. for 2005, by age:
AGE
Freq
Cu.F
( years )
(millions)
(millions)
0–9
7
7
10 – 19
8
15
20 – 29
7
22
30 – 39
9
31
40 – 49
9
40
50 – 59
8
48
60 – 69
6
54
70 – 79
4
58
80 – 89
2
60
Source: USA IDB
Points to notice:
• There is no gap between 9
and 10 as the data are
continuous.
• Points are plotted at upper
class boundaries (u.c.bs.)
e.g. the u.c.b. for 0 - 9
would normally be 9·5
The u.c.bs. for this data
set are 10, 20, 30, . . .
e.g. The projected population of the U.K. for 2005, by age:
AGE
f
Cu.f u.c.b.
( yrs )
(m)
(m)
( yrs )
0–9
7
7
10
10 – 19
8
15
20
20 – 29
7
22
30
30 – 39
9
31
40
40 – 49
9
40
50
50 – 59
8
48
60
60 – 69
6
54
70
70 – 79
4
58
80
80 – 89
2
60
90
Source: USA IDB
The projected population of the
U.K. for 2005 ( by age )
Age (yrs)