Sure, let's go through the solution step-by-step.
### Given Data:
- Total number of students: 40
- Frequency of students per instrument:
- Piano: 14
- Guitar: 10
- Violin: 8
- Drums: 8
### a) Finding the angle each student represents
First, to determine the angle that each student represents in a pie chart, we need to know how many degrees one student corresponds to. Since a full circle is 360 degrees, we divide the total degrees by the number of students:
[tex]\[
\text{Angle per student} = \frac{360 \text{ degrees}}{40} = 9 \text{ degrees per student}
\][/tex]
### b) Calculating the sector size for each category
Next, we multiply the angle per student by the number of students playing each instrument to find the sector size for each category.
1. Piano:
[tex]\[
\text{Sector size for Piano} = 14 \times 9 = 126 \text{ degrees}
\][/tex]
2. Guitar:
[tex]\[
\text{Sector size for Guitar} = 10 \times 9 = 90 \text{ degrees}
\][/tex]
3. Violin:
[tex]\[
\text{Sector size for Violin} = 8 \times 9 = 72 \text{ degrees}
\][/tex]
4. Drums:
[tex]\[
\text{Sector size for Drums} = 8 \times 9 = 72 \text{ degrees}
\][/tex]
### Summary of calculated sector sizes:
- Piano: 126 degrees
- Guitar: 90 degrees
- Violin: 72 degrees
- Drums: 72 degrees
### c) Drawing the pie chart
To draw the pie chart:
1. Draw a circle and make a full 360-degree division.
2. Use a protractor to measure and mark the sectors for each instrument based on the degrees calculated:
- Start from the top of the circle (usually taken as 0 degrees), measure and draw each sector in a clockwise direction.
- Mark the first sector of 126 degrees for Piano.
- From the end of the Piano sector, measure the next 90 degrees for Guitar.
- From the end of the Guitar sector, measure 72 degrees for Violin.
- The remaining section should naturally be 72 degrees for Drums, verifying our calculations.
Label each sector accordingly:
- Mark the section for Piano as 126 degrees.
- Mark the section for Guitar as 90 degrees.
- Mark the section for Violin as 72 degrees.
- Mark the section for Drums as 72 degrees.
This pie chart illustrates the distribution of students' instrument preferences at the music school.
