Questions: There are 54 students in a class. The Venn diagram below shows how many students play a sport, take a foreign language, do both, or do neither. Complete the following two-way frequency table.

There are 54 students in a class. The Venn diagram below shows how many students play a sport, take a foreign language, do both, or do neither.

Complete the following two-way frequency table.

Transcript text: There are 54 students in a class. The Venn diagram below shows how many students play a sport, take a foreign language, do both, or do neither. Complete the following two-way frequency table.

Solution

Solution Steps

Step 1: Identify the given values

Total students: 54
Students taking a foreign language and playing a sport: 21
Students taking a foreign language but not playing a sport: 17
Students playing a sport but not taking a foreign language: 12
Students neither taking a foreign language nor playing a sport: 4

Step 2: Calculate the total number of students taking a foreign language

Students taking a foreign language = Students taking a foreign language and playing a sport + Students taking a foreign language but not playing a sport
\( 21 + 17 = 38 \)

Step 3: Calculate the total number of students playing a sport

Students playing a sport = Students taking a foreign language and playing a sport + Students playing a sport but not taking a foreign language
\( 21 + 12 = 33 \)

Step 4: Fill in the two-way frequency table

Students taking a foreign language and playing a sport: 21
Students taking a foreign language but not playing a sport: 17
Students playing a sport but not taking a foreign language: 12
Students neither taking a foreign language nor playing a sport: 4

Final Answer

| | Plays a sport | Does not play a sport | Total | |---------------------------|---------------|-----------------------|-------| | Takes a foreign language | 21 | 17 | 38 | | Does not take a foreign language | 12 | 4 | 16 | | Total | 33 | 21 | 54 |

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