1. Types of Data Qualitative  Descriptive Quantitative  Numerical
Categories: colours, types of pets
Quantitative  Numerical
Discrete: countable
Continuous: measurable
We did qualitative, we did quantitative but only discrete – did grouped too last year – this year continuous  expressed as range using inequalities

2. Discrete vs Continuous
Count it or measure it?

3. Discrete Data CAN BE COUNTED (no intermediate values)
Data that can’t be broken down into fractions or decimals (like people – half a person, quarter of a person)
Often preceded by the words ‘number of’
number of people, number of pens in a pencil case, number of words in a book, shoe size (whole numbers)
Categorical: black, white, dog, cat …

4. (needs a measuring device)
Continuous Data
CAN BE MEASURED (range)
(needs a measuring device)
can be broken down into fractions or decimals to any degree of accuracy
heights, weights, lengths, volume, time, temperature, age (continuous because you don’t know the exact age)

5. How many cows are there in that field?
Discrete
Continuous

6. How fast can your car go?
Discrete
Continuous

7. How much water is there in this bottle?
Discrete
Continuous

8. How many CDs do you own?
Discrete
Continuous

9. What is your shoe size?
Discrete
Continuous

10. How much does a whale weigh?
Discrete
Continuous

11. What is the temperature of this fire?
Discrete
Continuous

12. How long does the bus to Valletta take?
Discrete
Continuous

13. How many goals have you scored this year?
Discrete
Continuous

14. Discrete Qualitative Continuous
What is the breed of that dog?
Discrete
Qualitative
Continuous

15. Discrete Continuous How much does a Mars Bar cost?
Can’t really be measured and can only take a set of distinct values can’t be 5euro
Discrete
Continuous

16. Here are the race times in seconds from a downhill race event (rounded to 1 d.p.)
Photo credit: © grynold, Shutterstock.com
The times range from about 85 to about 110 seconds: 110 – 85 = 25 seconds. There are lots of numbers in this range.
How can we group them up?

17. 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.
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?
Times in seconds
Frequency
85 – 90
90 – 95
95 – 100
100 – 105
105 – 110
Teacher notes
Students should see that some data types could have multiple entries on the table. If students do not see this, encourage them to work through the data list putting the times in the appropriate space. Discuss where 90.0, and should go. The table is ambiguous.
For discrete data it would be possible to edit the table to say 86 – 90, 91 – 95, 96 – 100, 101 – 105 etc (or 85 – 89, 90 – 94 etc) but for continuous data this would not work.
The students should use inequalities to firm up the boundaries of the data intervals.

18. Notation for class intervals
Teacher notes
Discuss more about the meaning of inequalities and how we can use them. Ask the students to tell you verbally what is meant by: 85 ≤ t < 90. Discuss where 90, 95 etc would go in this table. Represent the inequality on a number line. Ask pupils where numbers such as would go.
Note that the data has been rounded off to 1 d.p. so it could be argued that we could write the intervals as 85.0 – 89.9, 90.0 – 94.9 etc but this would imply that the data is discrete, so this would be incorrect.

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?
Teacher notes
Ask students to verbally tell you what times would be included in the class interval: 90 ≤ t < 95. They should answer something along the lines of: “this interval includes times larger than or equal to 90 seconds and less than 95 seconds” or “this interval includes times from 90 up to, but not including, 95 seconds”.
Ask students to verbally tell you what times would be included in the class interval: 105 ≤ t < 110. They should answer something along the lines of: “this interval includes times larger than or equal to 105 seconds and less than 110 seconds” or “this interval included times from 105 up to, but not including, 110 seconds”.
Pupils could work together in pairs to practise the correct use of vocabulary.

20. Draw a Frequency Table for this continuous data using class intervals
Here are the race times in seconds from a downhill race event.
Photo credit: © grynold, Shutterstock.com
Draw a Frequency Table for this continuous data using class intervals

21. To be able to distinguish between discrete and continuous data
By the end of the lesson we will be able to:
understand what discrete data is
understand what continuous data is
distinguish between discrete and continuous data
draw up a frequency table for continuous data