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

Discrete vs Continuous Count it or measure it?

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 …

(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 12.32456 heights, weights, lengths, volume, time, temperature, age (continuous because you don’t know the exact age)

How many cows are there in that field? Discrete Continuous

How fast can your car go? Discrete Continuous

How much water is there in this bottle? Discrete Continuous

How many CDs do you own? Discrete Continuous

What is your shoe size? Discrete Continuous

How much does a whale weigh? Discrete Continuous

What is the temperature of this fire? Discrete Continuous

How long does the bus to Valletta take? Discrete Continuous

How many goals have you scored this year? Discrete Continuous

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

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 . 123456789 Discrete Continuous

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?

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, 100.0 and 105.0 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.

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 99.9999999 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.

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.

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

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