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The bar chart and the pie chart

Statistics and probability, grade 10 (4 units) Lesson 3 of 20Learning

The bar chart and the pie chart

The bar chart

A bar chart has a bar for each value of the variable, and its height is the value’s frequency. It suits a qualitative variable and a discrete quantitative one.

How the 120 students of the first lesson get to school:

01020304050On footBy bikeBy school busBy carWay of getting to schoolStudents42183624
  • The horizontal axis: the values of the variable. The vertical axis: the frequency – here the number of students.
  • There are gaps between the bars, because the values are separate from each other.
  • The tallest bar shows the commonest value: on foot, 42 students.
  • The bars are easy to compare: twice as many students come by school bus as by bike, 3618=2\displaystyle {\frac{36}{18}}={2}.
The pie chart

A pie chart shows how a whole splits into parts. The whole circle is all the data, and each value is a slice. The slice’s angle is the value’s part of 360∘\displaystyle 360^{\circ}:

fn⋅360∘\displaystyle \frac{f}{n}\cdot360^{\circ}
Way of getting thereOn footBy bikeBy school busBy carTotal
Frequency42183624120
Angle126∘\displaystyle 126^{\circ}54∘\displaystyle 54^{\circ}108∘\displaystyle 108^{\circ}72∘\displaystyle 72^{\circ}360∘\displaystyle 360^{\circ}

For example, the slice “on foot”: 42120⋅360∘=126∘\displaystyle {\frac{42}{120}\cdot360^{\circ}}={126^{\circ}}.

35%On foot15%By bike30%By school bus20%By car
  • A pie chart shows at once what part of the whole each value is: “on foot” is a little more than a third of the circle, 35%.
  • The numbers themselves are not seen in it. Without the number of data you cannot tell from it how many students come on foot.
The double bar chart

A double bar chart compares two groups on the same variable: each value has two bars side by side, one for each group, in two colours.

Grade 10’s students were asked their favourite sport. The data are in percent of each group:

01020304050FootballBasketballSwimmingRunningFavourite sportPercent of the students4025152015203035BoysGirls
  • Among the boys football is the favourite sport, 40%; among the girls running, 35%.
  • Such a comparison is made in percent when the groups differ in size: with 80 boys and 120 girls, the numbers of students would not show what is commoner in each group.
  • In each group the bars add up to 100%.
When each chart suits

A chart is chosen by the kind of variable and by what is to be shown.

  • A bar chart – a qualitative or discrete quantitative variable with not too many values; good for comparing the frequencies.
  • A double bar chart – comparing two groups or more on the same variable.
  • A pie chart – parts of a whole: all the data split into a few values, and you want to see what part each one is. With many values the slices are small and hard to compare.
  • For a continuous quantitative variable, such as height, none of them suits: almost every datum is a different value. Next lesson – the histogram.
Exercise 1

A survey asked 50 households how many pets they have at home:

0510152001234Number of pets at homeHouseholds18151052
a

What percent of the households in the survey have no pets?

    / – 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 households have 2 pets or more?

      / – 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

      How many pets are there in all 50 households together?

        / – 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 students were asked their favourite subject:

        SubjectMathsEnglishPEArt
        Frequency128146

        The data are to be drawn as a pie chart.

        a

        What is the angle of the slice “PE”, in degrees?

          / – 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 angle of the slice “Art”, in degrees?

            / – 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 percent of the circle does the slice “Maths” take?

              / – 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 3

              A young new driver has to drive with a companion in the first months after getting a licence.
              A survey asked 1,200 parents of young new drivers how much they accompany their child on trips:

              52%On every trip30%On most trips13%On some trips5%Not at all
              a

              What is the variable, and what kind is it? What is the mode?

              b

              What percent of the parents do not accompany their child on every trip?

                / – 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

                How many times greater is the number of parents who accompany on every trip than the number who accompany on most trips? Round to two decimal places, and write ≈\displaystyle \approx before the rounded number.

                  / – 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

                  d

                  How many parents in the survey do not accompany their child at all?

                    / – 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

                    e

                    Could these data have been shown in a bar chart too? Explain.

                    Exercise 4

                    The same survey compared parents of daughters with parents of sons. The data are in percent of each group:

                    0102030405060On every tripOn most tripsOn some tripsNot at allHow much the parents accompanyPercent of the parents58281044632166DaughtersSons
                    a

                    Among the parents of daughters, 58% accompany on every trip; among the parents of sons, 46%. What is the difference between the two percents?

                      / – 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 two conclusions that can be drawn from the chart.

                      c

                      Why are the data in the chart in percent and not in numbers of parents?

                      Exercise 5

                      For each set of data, write which chart suits – bars, double bars, a pie or none of them – and explain why:

                      1. the number of goals in each of the team’s matches in the season;
                      2. how the class committee’s budget splits between a trip, a party and presents;
                      3. the blood types of the students of two classes, for comparing;
                      4. the weights of 200 babies born in a hospital.