Transcript Cumulative Frequency As its name suggests, we ADD the frequencies. The next table shows the number of stones of various masses and we will produce.

Cumulative Frequency
As its name suggests, we
ADD the frequencies.
The next table shows the number
of stones of various masses and
we will produce a cumulative
frequency diagram from this
data.
Cumulative Frequency
Example: The masses of stones are
recorded as follows:
Mass (Kg) frequency The 20 to 30 Kg
means that stones
0 to 20
0
weighed AT
20 to 30
3
LEAST
20Kg
but
30 to 40
5
less than 30 Kg
40 to 50
10
So the line should
50 to 60
8
read 20  m  30
60 to 70
4
This statement is also called the class
Cumulative Frequency
To convert this table to include cumulative
frequency, we add the frequencies as follows:
Mass (Kg)
Frequency Cumulative
Frequency
< 20
0
0
< 30
3
3
< 40
5
8
< 50
10
18
< 60
8
< 70
4
26
30
3+5=8
8 + 10= 18
We now plot the
mass (left
column) against
Cumulative
Frequency
Cumulative Frequency
Cumulative Frequency Curve
35
Always put the
Cumulative
Frequency (C.F.) on
the vertical axis!!
Cumulatuve Frequency
30
25
20
Plot C.F. against
the UPPER
BOUNDARY values
and join points
with a smooth line
15
10
5
0
20
30
40
50
Mass (Kg)
60
70
80
Cumulative Frequency
A cumulative frequency
graph produces a
characteristic ‘S’ shaped
curve!!
Cumulative Frequency
Now we have the Cumulative
Frequency curve, we can
determine Median, Upper
Quartile, Lower Quartile and
Inter Quartile Ranges.
Median is found from the mid
point of the frequency curve.
Cumulative Frequency
Cumulative Frequency Curve
Median value = 48 Kg
35
Cumulatuve Frequency
30
25
Half way on
the ‘Y’ axis
20
15
10
5
0
20
30
40
50
Mass (Kg)
60
70
80
Cumulative Frequency
Upper Quartile refers to the
value at ¾ or 75% up the
Cumulative Frequency axis.
Lower Quartile refers to the
value at ¼ or 25% up the
Cumulative Frequency axis.
Cumulative Frequency Curve
35
Cumulatuve Frequency
30
Upper Quartile
25
20
15
Lower Quartile
10
5
56
39
0
20
30
40
50
Mass (Kg)
60
70
80
As we now have the Quartile
values as well as median value,
we can work out:
The Inter-Quartile Range
The Inter-Quartile Range is:
Upper Quartile – Lower Quartile
(from the graph)
56 – 39 = 17
From this curve we can extract more
information including Box and
Whisker diagram.
Cumulative Frequency Curve
35
Cumulatuve Frequency
30
Upper Quartile
25
20
Median
15
Lower Quartile
10
5
0
20
30
40
50
60
70
Mass (Kg)
Minimum
L.Q.
M
U.Q.
Maximum
80
Box and Whisker Diagrams
Whenever we have two or more
cumulative frequency diagrams
to compare, it is better to
transfer the data to box and
whisker diagrams and compare
these.
The information is much easier
to compare in this form!!