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Probabillity and Statistics – Pie Chart

πŸ“˜ Notes

Pie Charts

A pie chart shows data as parts of a full circle. The full circle represents the whole amount, so the total angle is

\[ 360^\circ \]

To draw a pie chart, first find the total frequency, then work out each fraction or proportion, then convert each part into an angle.

Key facts and formulae

1. Find the total frequency

Add all the frequencies together.

\[ \text{Total frequency}=\text{sum of all frequencies} \]

2. Find the proportion or fraction

For each category,

\[ \text{Proportion}=\frac{\text{frequency}}{\text{total}} \]

3. Find the angle

Multiply the proportion by \(360^\circ\).

\[ \text{Angle}=\frac{\text{frequency}}{\text{total}}\times 360^\circ \]

4. Check

In a correct pie chart:

\[ \text{Total proportion}=1 \qquad \text{and} \qquad \text{Total angle}=360^\circ \]

Worked example

The table shows the favourite fruits of some students.

Apple Orange Banana Pear Total
Frequency 7 3 6 2 18
Proportion \(\dfrac{7}{18}\) \(\dfrac{3}{18}=\dfrac{1}{6}\) \(\dfrac{6}{18}=\dfrac{1}{3}\) \(\dfrac{2}{18}=\dfrac{1}{9}\) \(1\)
Angle \(140^\circ\) \(60^\circ\) \(120^\circ\) \(40^\circ\) \(360^\circ\)

Step 1: Find the total frequency

\[ 7+3+6+2=18 \]
Total frequency \(=18\)

Step 2: Find each proportion

Apple:

\[ \frac{7}{18} \]

Orange:

\[ \frac{3}{18}=\frac{1}{6} \]

Banana:

\[ \frac{6}{18}=\frac{1}{3} \]

Pear:

\[ \frac{2}{18}=\frac{1}{9} \]

These fractions should add up to \(1\).

Step 3: Find each angle

Apple:

\[ \frac{7}{18}\times 360^\circ=140^\circ \]

Orange:

\[ \frac{1}{6}\times 360^\circ=60^\circ \]

Banana:

\[ \frac{1}{3}\times 360^\circ=120^\circ \]

Pear:

\[ \frac{1}{9}\times 360^\circ=40^\circ \]

Check:

\[ 140^\circ+60^\circ+120^\circ+40^\circ=360^\circ \]

Step 4: Draw the pie chart with a protractor

Year 7 pie chart
  1. Draw a circle using a compass.
  2. Draw one radius from the centre to start.
  3. Use a protractor to measure the first angle, for example Apple \(140^\circ\).
  4. Draw the next sector from the new line, for example Orange \(60^\circ\).
  5. Continue with Banana \(120^\circ\) and Pear \(40^\circ\).
  6. Label each sector clearly.
  7. Add a title if needed.

Labels for the diagram

After drawing the sectors, label them clearly:

  • Apple β€” \(140^\circ\)
  • Orange β€” \(60^\circ\)
  • Banana β€” \(120^\circ\)
  • Pear β€” \(40^\circ\)

Common mistakes and exam tips

Common mistakes

  • Forgetting to find the total frequency first.
  • Using the wrong total when finding fractions.
  • Not multiplying by \(360^\circ\) to find the angle.
  • Drawing sectors inaccurately with the protractor.
  • Forgetting to label the sectors.

Exam tips

  • Always check that all frequencies add to the total.
  • Check that all proportions add to \(1\).
  • Check that all angles add to \(360^\circ\).
  • Use a sharp pencil and measure carefully with the protractor.
  • Write the category names neatly on or near the sectors.

Summary

\[ \text{Proportion}=\frac{\text{frequency}}{\text{total}} \] \[ \text{Angle}=\frac{\text{frequency}}{\text{total}}\times 360^\circ \]

To draw a pie chart, find the total, work out each fraction, change each fraction into an angle, then draw each sector carefully and label it.