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Sagot :
Sure, let’s complete the table by calculating the angles for each holiday destination and then proceed to draw the pie chart.
### Steps to Complete the Table:
1. Calculate the Total Frequency:
The total number of people is already given as 60.
2. Calculate the Angle for Each Destination:
- France:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of France}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{24}{60}\right) \times 360 = \frac{24 \times 360}{60} = 144^\circ \][/tex]
- Spain:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Spain}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{20}{60}\right) \times 360 = \frac{20 \times 360}{60} = 120^\circ \][/tex]
- Greece:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Greece}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{10}{60}\right) \times 360 = \frac{10 \times 360}{60} = 60^\circ \][/tex]
- Other:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Other}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{6}{60}\right) \times 360 = \frac{6 \times 360}{60} = 36^\circ \][/tex]
### Completed Table:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Holiday destinations} & \text{Frequency} & \text{Angle in } ^{\circ} \\ \hline \text{France} & 24 & 144^\circ \\ \hline \text{Spain} & 20 & 120^\circ \\ \hline \text{Greece} & 10 & 60^\circ \\ \hline \text{Other} & 6 & 36^\circ \\ \hline \end{array} \][/tex]
### Drawing the Pie Chart:
1. Draw a circle: Using a compass or a round object.
2. Draw a starting line: This line will serve as the starting point (reference point or the line from the center to the circumference).
3. Angle Measurements:
- Draw the first sector representing France with a [tex]\(144^\circ\)[/tex] angle in a clockwise direction.
- From the endpoint of the France sector, draw the next sector representing Spain with a [tex]\(120^\circ\)[/tex] angle.
- From the endpoint of the Spain sector, draw the Greece sector with a [tex]\(60^\circ\)[/tex] angle.
- The remaining sector represents 'Other' with a [tex]\(36^\circ\)[/tex] angle.
4. Label the Sectors: Label each sector with the corresponding destination and frequency.
### Visualization:
It would be best visualized with actual drawing tools or a software tool to plot it accurately. The angles should look something like:
- France: [tex]\(144^\circ\)[/tex] (largest sector)
- Spain: [tex]\(120^\circ\)[/tex] (second largest sector)
- Greece: [tex]\(60^\circ\)[/tex] (third largest sector)
- Other: [tex]\(36^\circ\)[/tex] (smallest sector)
Remember to keep the sectors neatly organized from the starting point, and make sure the sum of the angles equals [tex]\(360^\circ\)[/tex] in your pie chart.
This pie chart gives a clear visual representation of the different holiday destinations among the given people.
### Steps to Complete the Table:
1. Calculate the Total Frequency:
The total number of people is already given as 60.
2. Calculate the Angle for Each Destination:
- France:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of France}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{24}{60}\right) \times 360 = \frac{24 \times 360}{60} = 144^\circ \][/tex]
- Spain:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Spain}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{20}{60}\right) \times 360 = \frac{20 \times 360}{60} = 120^\circ \][/tex]
- Greece:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Greece}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{10}{60}\right) \times 360 = \frac{10 \times 360}{60} = 60^\circ \][/tex]
- Other:
[tex]\[ \text{Angle} = \left(\frac{\text{Frequency of Other}}{\text{Total Frequency}}\right) \times 360 = \left(\frac{6}{60}\right) \times 360 = \frac{6 \times 360}{60} = 36^\circ \][/tex]
### Completed Table:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Holiday destinations} & \text{Frequency} & \text{Angle in } ^{\circ} \\ \hline \text{France} & 24 & 144^\circ \\ \hline \text{Spain} & 20 & 120^\circ \\ \hline \text{Greece} & 10 & 60^\circ \\ \hline \text{Other} & 6 & 36^\circ \\ \hline \end{array} \][/tex]
### Drawing the Pie Chart:
1. Draw a circle: Using a compass or a round object.
2. Draw a starting line: This line will serve as the starting point (reference point or the line from the center to the circumference).
3. Angle Measurements:
- Draw the first sector representing France with a [tex]\(144^\circ\)[/tex] angle in a clockwise direction.
- From the endpoint of the France sector, draw the next sector representing Spain with a [tex]\(120^\circ\)[/tex] angle.
- From the endpoint of the Spain sector, draw the Greece sector with a [tex]\(60^\circ\)[/tex] angle.
- The remaining sector represents 'Other' with a [tex]\(36^\circ\)[/tex] angle.
4. Label the Sectors: Label each sector with the corresponding destination and frequency.
### Visualization:
It would be best visualized with actual drawing tools or a software tool to plot it accurately. The angles should look something like:
- France: [tex]\(144^\circ\)[/tex] (largest sector)
- Spain: [tex]\(120^\circ\)[/tex] (second largest sector)
- Greece: [tex]\(60^\circ\)[/tex] (third largest sector)
- Other: [tex]\(36^\circ\)[/tex] (smallest sector)
Remember to keep the sectors neatly organized from the starting point, and make sure the sum of the angles equals [tex]\(360^\circ\)[/tex] in your pie chart.
This pie chart gives a clear visual representation of the different holiday destinations among the given people.
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