WJEC MATHEMATICS
INTERMEDIATE
STATISTICS AND PROBABILITY
CUMULATIVE FREQUENCY
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Contents
Cumulative
Cumulative Frequency Graph
Quartiles
Interquartile Range
Box Plot
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Cumulative
'Cumulative' means to add up as you go along. Often you are asked
to turn a frequency table into a cumulative frequency table. Consider
this example showing the length of different pieces of string
Length
Frequency
21-24
3
25-28
7
29-32
12
33-36
6
37-40
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To turn this into a cumulative frequency table, we need a new
column, one that adds up the frequency column as it goes down.
Length Frequency
Cumulative Frequency
21-24
3
3
25-28
7
10 (3+7)
29-32
12
22 (3+7+12)
33-36
6
28 (3+7+12+6)
37-40
4
32 (3+7+12+6+4)
Cumulative Frequency Graph
Plot the cumulative
frequency against
the upper value in
each range.
JOIN THEM UP
WITH A CURVE LOOK FOR THE S
SHAPE
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Quartiles
Consider the
axis (the cumulative frequency axis).
 To find the lower quartile go one quarter of the way to the max
value
 To find the median go halfway to the max value
 To find the upper quartile go three quarters of the way up to the
max value
For the example on the previous page, the maximum value (the
biggest value in the cumulative frequency column) is 32.
So,
 One quarter of the way up will be at 8
 Half way up will be up at 16
 Three quarters of the way up will be at 24
Follow the arrows
across to the curve,
then drop down to
the x axis
LQ = 28
Median = 30
UQ = 33
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IMPORTANT
INTERQUARTILE RANGE = UQ - LQ
So, for our example,
Box Plots
Box and Whisker plots are used to display information about the
range, median, and quartiles.
This is how you construct the box and whisker plot
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Example
The oldest person in Mathsminster is 90. The youngest person is 15.
The median age of the residents is 44, the lower quartile is 25, and
the upper quartile is 67.
Represent this information with a box and whisker plot
Very often you will need to extract this information from a
cumulative frequency graph.
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Exam Questions S12
1.
7
2.
8
3.
9
4.
5.
10
6.
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