Question

A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.

Like soccer Do not like soccer Total
Like volleyball A D G
Do not like volleyball B E H
Total C F I


Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)

Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)

Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)

Answer 1

Part A)

Total number of students = 100
80 students like soccer. So this means 20 students do not like soccer.

Out of 80 who liked soccer, 30 liked volleyball, so this means remaining 50 do not like volleyball.

Out of 45 students who likes volleyball, 30 likes soccer (mentioned in previous statement), so 15 did not like soccer.

Based on this data, we can complete the table as shown in the image attached with.

Part B)

Number of students who do not like soccer = 20
Number of students who do not like volleyball = 55
This is also include 5 students who do not like both games.

So number of students who do not like either soccer or volleyball = 20 + 55 - 5 = 70 students

Percentage of students who do not like either soccer or volleyball = 70/100 = 70 %

Part C)

The survey reveals a greater dislike for volleyball.
80 students like soccer and only 45 students like volleyball.
Only 20 students do not like soccer, while 55 students do not like volleyball.

This shows a greater dislike for volleyball as compared to soccer.

Answer 2

Part A

The summary of the data in a two-way frequency table is given by


`\begin{center} \begin{tabular} {|p{3.2cm}|c|c|c|} &Like soccer&Do not like soccer&Total\\ [2ex] Like volleyball&30&15&45\\ [2ex] Do not like volleyball&50&5&55\\ [2ex] Total&80&20&100 \end{tabular} \end{center}`


Part B:

From the table above it can be seen that 5 out of the 100 survey respondents did not like either soccer or volleyball.

Therefore, the percentage of survey respondents who did not like either soccer or volleyball is 5%.


Part C

From the table it can be seen that while 20 respondents did not like soccer, 55 respondents did not like volleyball.

This shows that there is a greater dislike for volleyball than for soccer.