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Cambridge IGCSE0607

Discrete and continuous data

International Mathematics 0607 Chapter Notes

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Discrete and continuous data
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Discrete and continuous data notes

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In this chapter

  1. 1Discrete data
  2. 2Continuous data
  3. 3Telling them apart

1. Discrete data

Discrete data take discrete numerical values. If you can count something, it is discrete data, and a count can only be an integer.

The number of candidates in a class, the number of siblings and the number of books are all discrete. So are a shoe size and an age in complete years.

A question about gender, hair colour or eye colour cannot be answered with a number. These are qualitative data, not discrete data.

Examiner insight

“Discrete data examples include the number of candidates in a class, number of siblings or number of books. A helpful idea is that if data includes, ‘number of’ then it is discrete data.” “Many put answers asking for the person’s gender or hair colour.”

Worked example 12 marks

A teacher records the number of books that each student in her class read this term. State whether these data are discrete or continuous. Give a reason.

  1. 1

    discrete [1]

  2. 2

    the data only take integer values [1]

2. Continuous data

Continuous data are measured on a continuous scale.

Time, height, mass, speed and capacity are all continuous. You measure them with a ruler or against another scale.

Weight, distance, kilometres per litre and maximum speed are continuous too.

Examiner insight

“Types of continuous data include time (used in the question), height, mass, speed and capacity.” “For part (b), the weight of an apple is continuous as it is measured on a continuous scale like height, distance and time.”

Worked example 12 marks

The mass of each apple picked from a tree is found using scales. State whether these data are discrete or continuous. Give a reason.

  1. 1

    continuous [1]

  2. 2

    mass is measured on a continuous scale [1]

3. Telling them apart

Ask one question: do I count it or do I measure it?

Counted data are discrete. Measured data are continuous.

When a question asks you to give a reason, describe the type of numbers used in the data. Say that the data only take integer values, or that they are measured on a continuous scale.

Examiner insight

“Candidates need a way of remembering the difference between discrete and continuous data – for example, if you can count something it is discrete data (e.g. numbers of siblings), if you measure something with a ruler or against another scale, it is continuous data (e.g. your height).” “For part (a), many answered with discrete but were not able to give an acceptable reason.”

Worked example 13 marks

Classify each type of data as discrete or continuous.

(a) The shoe size of a student.(b) The speed of a cyclist.(c) The number of candidates in a class.

  1. 1

    (a) discrete, as a shoe size takes separate numerical values [1]

  2. 2

    (b) continuous, as speed is measured against a scale [1]

  3. 3

    (c) discrete, as the candidates are counted [1]

Recap

  • Discrete data take discrete numerical values. If you can count it, it is discrete.
  • Continuous data are measured on a continuous scale.
  • Time, height, mass, speed and capacity are continuous.
  • Number of siblings, books or candidates, shoe size and age in complete years are discrete.
  • Eye colour, hair colour and gender are qualitative data, not discrete data.
  • Give the type of numbers as the reason: integer values, or measured on a continuous scale.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. State whether the number of brothers and sisters a student has is discrete or continuous.1 mark
  2. State whether the height of a sunflower is discrete or continuous.1 mark
  3. Classify each as discrete or continuous. (a) The number of seats in a hall. (b) The time taken to run 100 m. (c) A student's shoe size. (d) The mass of a parcel.4 marks
  4. The number of goals a team scores in each match is recorded. State the type of data, with a reason.2 marks
  5. Alex is surveying his class. Write a question he could ask that gives discrete data.1 mark
  6. A person's age in complete years is recorded. State the type of data, with a reason.2 marks
  7. A garage records these four items about its cars. Tick one box in each row to show whether the data are discrete or continuous. | Item | Discrete | Continuous | | --- | --- | --- | | Number of doors | | | | Capacity of the fuel tank | | | | Maximum speed | | | | Number of cars sold in a week | | |2 marks
  8. A weather station measures the rainfall each day in mm. It also counts the number of days in each month with rain. State which of the two sets of data is discrete. Give a reason for each set.3 marks
  9. A clinic counts the patients it sees on each of 10 days: 14, 9, 12, 15, 11, 9, 13, 16, 10, 15. The mean is 12.4 patients per day. (a) State whether the data are discrete or continuous. (b) Maya says the data stop after 10 days, so they are not continuous. Explain why this is not an acceptable reason, and give an acceptable one. (c) Ravi says the mean, 12.4, is not a whole number, so the data are continuous. Explain why Ravi is wrong.5 marks
  10. A cycle hire shop records five things for each hire. P: the number of gears on the bicycle. Q: the distance ridden, in km. R: the colour of the bicycle. S: the age of the rider in complete years. T: the maximum speed reached, in km / h. (a) For each of P, Q, R, S and T, state whether the data are discrete, continuous or neither. (b) Write a question the shop could ask to get one more item of discrete data about the rider.6 marks

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