Question

Mrs. Webster surveyed her class of 20 students. She asked each student to identify his or her favorite sport out of a list of five sports. Each student could only choose one sport and everyone participated. The results of the survey are shown in the chart. $$ \begin{array}{|l|l|} \hline \text { Football } & 8 \\ \hline \text { Basketball } & 5 \\ \hline \text { Baseball } & 4 \\ \hline \text { Soccer } & 2 \\ \hline \text { Hockey } & 1 \\ \hline \end{array} $$ If five more students join the class and all five chose soccer as their favorite sport, what percent of the class now favors soccer? A. \(10 \%\) B. \(28 \%\) C. \(32 \%\) D. \(35 \%\)

Short answer

B. \( 28\text{%} \)

Step-by-step solution

Determine the initial number of students

There are initially 20 students in the class.

Calculate the new number of students

Five more students join the class, so the new total number of students is: \[ 20 + 5 = 25 \]

Determine initial number of students favoring soccer

From the survey chart, 2 students initially favored soccer.

Update the number of students favoring soccer with new joiners

All five new students chose soccer, so the new number of students who favor soccer is: \[ 2 + 5 = 7 \]

Calculate the percentage of the class that favors soccer

To find the percentage of the class that now favors soccer, use the formula: \[ \text{Percentage} = \left(\frac{\text{Number who favor soccer}}{\text{Total number of students}}\right) \times 100 \] Plugging in the values: \[ \text{Percentage} = \left(\frac{7}{25}\right) \times 100 = 28\text{%} \]

Select the correct answer

The percentage of the class that now favors soccer is 28%. Therefore, the correct answer is B. \( 28\text{%} \)

Key concepts

Survey Results Analysis

Understanding survey results involves carefully examining the data collected. In the given exercise, Mrs. Webster surveyed her students to find out their favorite sport. Each student could only choose one sport, and every student participated. This is important because it ensures the data represents the entire class.
Key steps to analyze the survey results are:

• List all the options provided (Football, Basketball, Baseball, Soccer, Hockey)
• Record the number of students choosing each option
• Summarize the total votes for easy comparison

Analyzing survey results helps in understanding preferences and making informed decisions. In our example, it helps Mrs. Webster understand which sports her students prefer the most.

Student Population Changes

Student population changes can significantly affect data analysis. In our exercise, five more students joined the class, changing the total number of students from 20 to 25.
Here’s how we handle changes in population:

• Identify the initial population (20 students)
• Add the new members (5 more students)
• Recalculate the total population (20 + 5 = 25 students)

It’s crucial to include all students in the updated total to ensure accurate analysis. For example, five new students all chose soccer as their favorite sport. This specific change directly impacts our calculations and the conclusion we derive from the updated data. Ensuring clarity in population changes helps maintain the accuracy and reliability of the survey results.

Calculating Percentages

Calculating percentages is an essential skill in data analysis. In our exercise, we needed to find the new percentage of students who favor soccer after five new students joined the class.
To calculate percentages, follow these steps:

• Identify the number of students favoring soccer (initially 2)
• Add new joiners favoring soccer (5 new students)
• Find the updated total number of students favoring soccer (2 + 5 = 7)
• Divide the number of soccer fans by the new total student number (7/25)
• Multiply the result by 100 to get the percentage \[ \text{Percentage} = \frac{7}{25} \times 100 = 28\text{%} \]

This simple formula helps us understand the relative size of a part in comparison to the whole. In our case, 28% of the class now favors soccer. Understanding how to correctly calculate percentages is crucial for analyzing survey results and making informed decisions based on the data.