Question

the following table shows the results of a survey of 200 people about their favorite sport: soccer: 60 people basketball: 40 people baseball: 50 people tennis: 20 people swimming: 30 people tasks: 1. construct a circle graph. 2. which sport is the most popular? 3. what percentage of people prefer tennis? 4. how many degrees represent swimming? a survey of 60 students was conducted about their favorite fruits. the results are below: apple: 18 students; banana: 12 students; orange: 15 students; mango: 9 students; grapes: 6 students. tasks: 1. draw a circle graph to represent this data. 2. what fraction of students prefer bananas? 3. which fruit was chosen by exactly one - quarter of the students? 4. how many degrees of the circle does \apple\ represent?

Explanation:

5.

Step1: Construct a circle graph

Draw a circle. Then, for each sport, calculate the central - angle of the sector representing it. The total number of people surveyed is $n = 200$. The central - angle of a sector is given by $\theta=\frac{\text{Number of people for a sport}}{\text{Total number of people}}\times360^{\circ}$.

Step2: Determine the most popular sport

We compare the number of people who prefer each sport. Since $60>50 > 40>30>20$, soccer is the most popular sport.

Step3: Calculate the percentage of people who prefer tennis

The number of people who prefer tennis is $20$. The percentage is $\frac{20}{200}\times100\% = 10\%$.

Step4: Calculate the degrees representing swimming

The number of people who prefer swimming is $30$. The central - angle $\theta=\frac{30}{200}\times360^{\circ}=54^{\circ}$.

Step1: Draw a circle graph

Draw a circle. For each fruit, calculate the central - angle of the sector representing it. The total number of students surveyed is $n = 60$. The central - angle of a sector is given by $\theta=\frac{\text{Number of students for a fruit}}{\text{Total number of students}}\times360^{\circ}$.

Step2: Find the fraction of students who prefer bananas

The number of students who prefer bananas is $12$, and the total number of students is $60$. The fraction is $\frac{12}{60}=\frac{1}{5}$.

Step3: Determine the fruit chosen by one - quarter of the students

One - quarter of $60$ is $\frac{1}{4}\times60 = 15$. The fruit chosen by $15$ students is orange.

Step4: Calculate the degrees of the circle that "Apple" represents

The number of students who prefer apples is $18$. The central - angle $\theta=\frac{18}{60}\times360^{\circ}=108^{\circ}$.

Answer:

1. (The construction of the circle graph should be done by drawing sectors with appropriate central - angles for each sport).
2. Soccer
3. $10\%$
4. $54^{\circ}$

6.