Question

1. greg works as a tour guide. he tracks how tourists heard about the tours.

• 60% took the tour as part of a travel package;
• 15% had the tour recommended by the local tourism office;
• 10% came based on the recommendation of a friend; and
• the remainder were walk - ins.

draw a circle graph to display the data. show all calculations.

Explanation:

Step1: Find the percentage of walk - ins

The sum of all percentages should be \(100\%\). Let \(x\) be the percentage of walk - ins. Then \(x=100-(60 + 15+10)\)
\(x = 15\%\)

Step2: Calculate the central angles

The central angle \(\theta\) of a sector in a circle graph is given by \(\theta=\text{Percentage}\times360^{\circ}\)

• For travel package (\(60\%\)): \(\theta_1=0.6\times360^{\circ}=216^{\circ}\)
• For local tourism office recommended (\(15\%\)): \(\theta_2 = 0.15\times360^{\circ}=54^{\circ}\)
• For friend recommended (\(10\%\)): \(\theta_3=0.1\times360^{\circ}=36^{\circ}\)
• For walk - ins (\(15\%\)): \(\theta_4=0.15\times360^{\circ}=54^{\circ}\)

Step3: Draw the circle graph

Use a protractor to draw sectors with the calculated angles and label them.

Answer:

To draw a circle graph (pie - chart), we first need to find the percentage of walk - ins. Then calculate the central angles for each category.
The percentage of walk - ins: \(100-(60 + 15+10)=15\%\)

The formula for the central angle of a sector in a circle graph is \(\theta=\text{Percentage}\times360^{\circ}\)

For the travel - package category (\(60\%\)):
\(\theta_1 = 60\%\times360^{\circ}=0.6\times360^{\circ}=216^{\circ}\)

For the local - tourism - office - recommended category (\(15\%\)):
\(\theta_2=15\%\times360^{\circ}=0.15\times360^{\circ} = 54^{\circ}\)

For the friend - recommended category (\(10\%\)):
\(\theta_3=10\%\times360^{\circ}=0.1\times360^{\circ}=36^{\circ}\)

For the walk - in category (\(15\%\)):
\(\theta_4 = 15\%\times360^{\circ}=0.15\times360^{\circ}=54^{\circ}\)

Now, we can draw the circle graph:

1. Draw a circle.
2. Use a protractor to measure and draw the sectors with the calculated central angles (\(216^{\circ}\), \(54^{\circ}\), \(36^{\circ}\), \(54^{\circ}\))
3. Label each sector with its corresponding category (travel package, local tourism office recommended, friend recommended, walk - ins)