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© Boardworks Ltd 20101 of 19
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© Boardworks Ltd 20102 of 19
© Boardworks Ltd 20103 of 19
Discrete and continuous data
Discrete data is data that can only take certain values, such as the number of spectators at a sporting event.
Numerical data can come in a wide variety of different forms.
Continuous data can take any value and still have a meaning, such as the height of different trees in a forest.
Can you think of other examples of discrete and continuous data?
© Boardworks Ltd 20104 of 19
Continuous data
Don Lippincott was the holder of the first world 100 metre sprint record. In 1912, he ran 100 m in 10.6 seconds.
The second fastest woman in the world in the 100 metre sprint in 2009 was Carmelita Jeter. She ran 100 m in a time of 10.64 seconds.
Is it possible to tell who was the fastest?
What unit has each time been rounded to?
Would it be possible for someone to get a time rounded to the nearest thousandth of a second if we had sensitive enough equipment?
© Boardworks Ltd 20105 of 19
Tom regularly takes part in downhill cycle races.
Analysing data
How accurately has he measured this time?
Is the data continuous or discrete?
Tom’s best time is 101.6 seconds.
He records the race times of all the competitors in a race on a spreadsheet.
© Boardworks Ltd 20106 of 19
If you wanted to analyze the performances, what could you do with the data?
How easy is the data to analyze in this format?
Can you draw any conclusions?
Analysing data
Here are the race times in seconds from a downhill race event.
88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5
95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3
97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4
98.5 98.9 99.0 99.1 99.6 99.6 99.8 100.0100.6
100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8101.9
102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1105.0
105.2 105.6 105.6 105.7 105.8 105.9
© Boardworks Ltd 20107 of 19
Obtaining information
© Boardworks Ltd 20108 of 19
© Boardworks Ltd 20109 of 19
Choosing the right graph
© Boardworks Ltd 201010 of 19
A student used a spreadsheet program to produce a graph of the race data.
Choosing the right graph
Here, you can see the bar chart he printed to display the data.
What labels could be added to the axes?
What does the graph show?
Is it an appropriate graph? 80.0
85.0
90.0
95.0
100.0
105.0
110.0
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The best graph?
© Boardworks Ltd 201012 of 19
© Boardworks Ltd 201013 of 19
Grouping data
A list of results is called a data set and it is often easier to analyze a large data set if the data is put into groups.
The widths of the groups are called class intervals.
You can then use this information to draw a frequency diagram or a histogram.
Before drawing the diagrams, you need to decide on the size of each class interval so that there are between 5 and 10 class intervals.
What is the best size for the class intervals for the race times data?
© Boardworks Ltd 201014 of 19
Class intervals
The times range from about 85 to about 110 seconds: 110 – 85 = 25 seconds.
We could use class intervals with a width of 5 seconds: 25 ÷ 5 = 5 class intervals.
Here are the race times in seconds from a downhill race event.
88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5
95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3
97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4
98.5 98.9 99.0 99.1 99.6 99.6 99.8 100.0100.6
100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8101.9
102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1105.0
105.2 105.6 105.6 105.7 105.8 105.9
© Boardworks Ltd 201015 of 19
What is wrong with this table?
How should the class intervals be written down?
How can your knowledge of inequalities help you to create better class intervals?
Notation for class intervals
Tom decides to create his own groups and draws a table with class intervals that he thinks fit the race data.
Times in seconds Frequency
85 – 90
90 – 95
95 – 100
100 – 105
105 – 110
© Boardworks Ltd 201016 of 19
Notation for class intervals
© Boardworks Ltd 201017 of 19
Notation for class intervals
85 ≤ t < 90 will include times that are ‘larger than or equal to 85 seconds and less than 90 seconds’.
Another way to say this is that this class interval includes times ‘from 85 seconds up to, but not including, 90 seconds”
What times will be included within this class interval: 90 ≤ t < 95?
What times will be included within this class interval: 105 ≤ t < 110?
© Boardworks Ltd 201018 of 19
Notation for class intervals
© Boardworks Ltd 201019 of 19
100 ≤ t < 105
105 ≤ t < 110
95 ≤ t < 100
90 ≤ t < 95
85 ≤ t < 90
Time in seconds Frequency
Class intervals
Use the data from Tom’s race times to fill in the table.
What graph would you use to represent this data? 19
7
28
5
1
88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5
95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3
97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4
98.5 98.9 99.0 99.1 99.6 99.6 99.8 100.0100.6
100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8101.9
102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1105.0
105.2 105.6 105.6 105.7 105.8 105.9
