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Relative frequency

Data and chance, grade 6 Lesson 3 of 9Learning

Relative frequency

Relative frequency

The relative frequency of an answer is its part of all the data: its frequency, divided by the number of all the data.

fn\displaystyle \frac{f}{n}
  • f\displaystyle f – the answer’s frequency.
  • n\displaystyle n – the number of all the data.
  • Class 6A has 20 pupils, and 7 of them chose PE as their favourite subject. The relative frequency of PE is 720\displaystyle \frac{7}{20}.
A fraction, a decimal and a percentage

A relative frequency can be written as a fraction, a decimal or a percentage – it is the same number: 720=35100=0.35=35%\displaystyle {\frac{7}{20}}={\frac{35}{100}}={0.35}={35\%}.
This is the whole table of 6A’s favourite subjects:

SubjectmathsPEartscienceEnglish
Frequency57332
Relative frequency520=25%\displaystyle {\frac{5}{20}}={25\%}720=35%\displaystyle {\frac{7}{20}}={35\%}320=15%\displaystyle {\frac{3}{20}}={15\%}320=15%\displaystyle {\frac{3}{20}}={15\%}220=10%\displaystyle {\frac{2}{20}}={10\%}

A percentage shows at once how many in every hundred: 35% – 35 in every 100 pupils.

The relative frequencies’ sum

All the relative frequencies add up to 1, that is 100%:

25%+35%+15%+15%+10%=100% 25\%+35\%+15\%+15\%+10\%=100\%
  • The reason: the frequencies add up to the number of all the data, so the fractions add up to 2020=1\displaystyle {\frac{20}{20}}={1}.
  • It is a good check: a sum other than 100% means a mistake in the working.
Comparing groups

Relative frequency compares groups of different sizes.
Class 6A has 20 pupils, and 7 of them chose PE.
Class 6C has 30 pupils, and 9 of them chose PE.

  • In 6C more pupils chose PE: 9 against 7.
  • But the relative frequency: in 6A 720=35%\displaystyle {\frac{7}{20}}={35\%}, and in 6C 930=30%\displaystyle {\frac{9}{30}}={30\%}.
  • So in 6A a larger part of the class chose PE.
From relative frequency to frequency

When you know the relative frequency and the number of all the data, you find the frequency by multiplying.
A class has 30 pupils, and 40% of them come by bus:

40%×30=40100×30=12 40\%\times30=\frac{40}{100}\times30=12

12 pupils come by bus.

Exercise 1

A class has 25 pupils, and 10 of them have a dog.
What is the relative frequency of the pupils who have a dog?

a

Write it as a fraction in its lowest terms.

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

    Write it as a percentage.

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      Exercise 2

      40 pupils answered the question “How do you get to school?”:

      The waywalkbusbikecar
      Frequency161086
      a

      What is the relative frequency of “walk”? Write it as a decimal.

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        b

        What is the relative frequency of “bus”? Write it as a percentage.

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          c

          What do the relative frequencies of all the ways add up to?
          Explain without working them out.

          Exercise 3

          Class 6A has 30 pupils, and 12 of them play a musical instrument.
          Class 6B has 20 pupils, and 10 of them play a musical instrument.
          In which class does a larger part of the pupils play?
          Explain with the relative frequencies.

          Exercise 4

          50 pupils chose their favourite food.
          The relative frequency of pizza is 0.3.
          How many pupils chose pizza?

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            Exercise 5

            60 pupils chose their favourite season.
            One relative frequency is missing from the table:

            Seasonwinterspringsummerautumn
            Relative frequency0.350.25?0.1
            a

            What is the relative frequency of summer?

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              b

              How many pupils chose winter?

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power