Question

solve the problem.
a group of junior-high athletes was asked what team sport was their favourite. the data are summarized in the table below. on the pie chart, which area would correspond to the category \volleyball\?

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$$\begin{tabular}{|l|l|} \\hline team sport & frequency \\\\ \\hline soccer & 12 \\\\ \\hline volleyball & 28 \\\\ \\hline basketball & 20 \\\\ \\hline football & 20 \\\\ \\hline \\end{tabular}$$

select one:
a. area d
b. area a
c. area c
d. area b

Explanation:

Calculate the total frequency

Find the sum of all frequencies.

$$ \text{Total} = 12 + 28 + 20 + 20 = 80 $$

Determine the proportions

Calculate the percentage for each sport.

$$ \text{Soccer} = \frac{12}{80} = 15\% $$

$$ \text{Volleyball} = \frac{28}{80} = 35\% $$

$$ \text{Basketball} = \frac{20}{80} = 25\% $$

$$ \text{Football} = \frac{20}{80} = 25\% $$

Analyze the pie chart sectors

Compare the calculated percentages to the visual sectors.

• Two sectors are exactly equal to \(25\%\) (quarter circles): Area C and Area D.
• One sector is smaller than \(25\%\): Area A.
• One sector is larger than \(25\%\): Area B.

Match Volleyball to its sector

Identify the sector representing \(35\%\).

• Volleyball has the largest frequency (\(35\%\)).
• Area B is the only sector larger than a quarter circle.
• Therefore, Volleyball corresponds to Area B.

Answer:

• a Area D
• b Area A
• c Area C
• d Area B (Correct answer)