
Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:



Favorite Sport SwimmingRunningVolleyballRow totalsGrade 8

0.14

0.18

0.22

0.54

Grade 9

0.17

0.24

0.05

0.46

Column totals

0.31

0.42

0.27

1



Based on the data, which statement is **most likely** correct? (1 point)

In Grade 8, 14 students liked swimming.

In Grade 9, 31% of students liked swimming.

In Grade 8, 22% of students liked volleyball.

In Grade 9, 5 students liked volleyball.

Let's analyze each statement based on the relative frequency table provided:

1. **In Grade 8, 14 students liked swimming.**  
   This statement mentions an absolute number of students (14), but the table provides relative frequencies, not actual numbers. The relative frequency for swimming in Grade 8 is **0.14** (14%), but without knowing the total number of students in Grade 8, we cannot confirm that exactly 14 students liked swimming. Thus, this statement is **unlikely**.

2. **In Grade 9, 31% of students liked swimming.**  
   The table shows that the relative frequency of students who liked swimming in Grade 9 is **0.17**, which is **17%**, not 31%. Therefore, this statement is **incorrect**.

3. **In Grade 8, 22% of students liked volleyball.**  
   According to the table, the relative frequency for volleyball in Grade 8 is **0.22**, or 22%, which matches the statement exactly. This statement is **correct**.

4. **In Grade 9, 5 students liked volleyball.**  
   The relative frequency of students who liked volleyball in Grade 9 is **0.05**, or 5%. However, without knowing the total number of students in Grade 9, we can't confirm that this translates to exactly 5 students. This statement is **uncertain** without more information.

### Conclusion:
The **most likely** correct statement is:
- **In Grade 8, 22% of students liked volleyball.**

Would you like more details on this? Here are five related questions for further exploration:

1. How do we calculate the number of students based on relative frequencies?
2. How can we interpret the row and column totals in this table?
3. If Grade 8 had 50 students, how many liked swimming?
4. Why is it important to know the total number of students when working with relative frequencies?
5. What can we infer about the overall preference for volleyball between Grade 8 and Grade 9?

**Tip**: Always ensure you know the total population when working with relative frequencies to convert percentages to actual numbers.

Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:

Favorite Sport SwimmingRunningVolleyballRow totalsGrade 8

0.14

0.18

0.22

0.54

Grade 9

0.17

0.24

0.05

0.46

Column totals

0.31

0.42

0.27

1

Based on the data, which statement is most likely correct?

In Grade 8, 14 students liked swimming.
In Grade 9, 31% of students liked swimming.
In Grade 8, 22% of students liked volleyball.
In Grade 9, 5 students liked volleyball.

Analyze the relative frequency table of favorite sports among Grade 8 and Grade 9 students. Learn how to interpret the data and determine the most accurate statement, such as 22% of Grade 8 students preferring volleyball. Ideal for Grades 6-8.

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