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Cambridge IGCSE0607

Classifying statistical data

International Mathematics 0607 Chapter Notes

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Classifying statistical data
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Classifying statistical data notes

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In this chapter

  1. 1Types of data
  2. 2Tally tables and frequency tables
  3. 3Two-way tables

1. Types of data

Data that are not numbers, such as eye colour or hair colour, are qualitative (categorical). They cannot be answered with a number.

Numerical data are discrete or continuous. If you count something, it is discrete data: the number of siblings, books or seats. Counted data only takes on integer values. Shoe size and age in complete years are also discrete.

If you measure something against a scale, it is continuous data: height, mass, time, speed or capacity.

When you give a reason, describe the type of numbers. "The data stops after 10 days" is not a reason.

Examiner insight

“For part (a), many answered with discrete but were not able to give an acceptable reason.” “A helpful idea is that if data includes, 'number of' then it is discrete data.”

Worked example 13 marks

Write discrete or continuous for each set of data.

(a) The number of seats in a car.

(b) The maximum speed of a car.

(c) The time taken to run 100 m.

  1. 1

    (a) seats are counted, so discrete [1]

  2. 2

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

  3. 3

    (c) time is measured on a continuous scale, so continuous [1]

2. Tally tables and frequency tables

A tally table records data as it is collected, with one tally mark for each item.

A frequency table shows how many times each value or category occurs. Count the tally marks in each row and write the number in the frequency column. A tally alone is not the answer.

Add the frequencies. The total must equal the number of items in the data.

Examiner insight

“A few gave only a tally and there were some examples of miscounting.”

Worked example 13 marks

Twenty pupils were asked how many pets they have. The answers were

1, 0, 2, 1, 1, 3, 0, 2, 1, 2, 0, 1, 1, 2, 4, 1, 0, 2, 1, 3.

Complete a frequency table for the data.

  1. 1

    count each value: 0 occurs 4 times, 1 occurs 8 times, 2 occurs 5 times [1]

  2. 2

    3 occurs 2 times and 4 occurs 1 time [1]

  3. 3

    check: 4 + 8 + 5 + 2 + 1 = 20, which is the number of pupils [1]

3. Two-way tables

A two-way table sorts the same data by two features at once. One feature gives the rows and the other gives the columns.

Each row and each column has a total. The row totals and the column totals both add to the same overall total.

Fill in the cells you can work out from a row or column total. Then use those cells to find the rest.

Worked example 13 marks

A club has 40 members. 22 are boys. 15 members are under 16, and 9 of these are boys. Find the number of girls who are 16 or over.

Under 1616 or overTotal
Boys922
Girls
Total1540
  1. 1

    girls in total = 40 - 22 = 18 [1]

  2. 2

    girls under 16 = 15 - 9 = 6 [1]

  3. 3

    girls 16 or over = 18 - 6 = 12 [1]

Recap

  • Qualitative data cannot be answered with a number, such as hair colour.
  • Count it: discrete. Measure it: continuous.
  • 'Number of' means discrete data. Time, height, mass, speed and capacity are continuous.
  • A reason for counted data being discrete: it only takes on integer values.
  • A frequency table gives the count for each value. The counts add to the number of items.
  • A two-way table sorts data by two features, with row and column totals.

End-of-chapter exercise

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

  1. Write discrete or continuous for the number of books in a bag.1 mark
  2. Name the type of data that hair colour gives.1 mark
  3. Write discrete or continuous for (a) the mass of a parcel, (b) the shoe size of a pupil.2 marks
  4. Do not use a calculator. Ten pupils scored 3, 1, 2, 3, 3, 2, 1, 3, 2, 3 in a quiz. Complete a frequency table for the scores 1, 2 and 3.3 marks
  5. Do not use a calculator. A frequency table for 20 cars shows 7 red, 5 blue and the rest green. How many cars are green?2 marks
  6. Explain why the time taken to run 100 m is continuous data.1 mark
  7. Do not use a calculator. 30 pupils were asked how they travel to school. Each pupil either walks or travels by bus. 18 are girls. 12 pupils walk, and 7 of these are boys. Find the number of girls who travel by bus. | | Walk | Bus | Total | | --- | --- | --- | --- | | Boys | 7 | | | | Girls | | | 18 | | Total | 12 | | 30 |2 marks
  8. Do not use a calculator. A shop records 80 sales. 52 were paid by card and the rest by cash. 31 sales were for more than 20 dollars. 19 of the cash sales were for more than 20 dollars. Find the number of card sales that were for 20 dollars or less.4 marks
  9. Do not use a calculator. A vet records each of 90 animals as a dog, a cat or a rabbit, and as male or female. 48 are dogs. There are twice as many cats as rabbits. 50 of the animals are male. 26 dogs are male and 9 rabbits are female. Find the number of female cats.5 marks
  10. A bus company keeps records for its 25 drivers. (a) It records each driver's age in complete years and the time each driver takes to drive one route. For each, write discrete or continuous and give a reason. (b) The table shows the number of late arrivals for each driver in one week. The frequency for 0 late arrivals is three times the frequency for 3 late arrivals. Find the number of drivers who had fewer than 2 late arrivals. | Late arrivals | 0 | 1 | 2 | 3 | | --- | --- | --- | --- | --- | | Frequency | | 9 | 4 | |5 marks

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