A sample of 200 college freshmen was asked how many hours per week they spent playing video games. The following frequency distribution presents the results.

Question

1.0-7.9 hours with a frequency of 26
8.0-14.9 hours with a frequency of 40
15.0-21.9 hours with a frequency of 48
22.0-28.9 hours with a frequency of 25
29.0-35.9 hours with a frequency of 20
36.0-42.9 hours with a frequency of 15
43.0-49.9 hours with a frequency of 10
50.0-56.9 hours with a frequency of 5
57.0-63.9 hours with a frequency of 3
64.0-70.9 hours with a frequency of 8

How many classes are there?
What is the class width?
Do not round.

(c) What percentage of students play video games for less than 15 hr per week?
D) what percentage plays for 8 or more hours per week?

Answer 1

To answer your questions, let's first break down the information provided.

Step 1: Determine the number of classes and class width

Classes: The number of classes can be counted directly from the frequency distribution presented:

1. 1.0-7.9 hours (Frequency = 26)
2. 8.0-14.9 hours (Frequency = 40)
3. 15.0-21.9 hours (Frequency = 48)
4. 22.0-28.9 hours (Frequency = 25)
5. 29.0-35.9 hours (Frequency = 20)
6. 36.0-42.9 hours (Frequency = 15)
7. 43.0-49.9 hours (Frequency = 10)
8. 50.0-56.9 hours (Frequency = 5)
9. 57.0-63.9 hours (Frequency = 3)
10. 64.0-70.9 hours (Frequency = 8)

Total Classes = 10

Class Width: The class width can be determined by taking the difference between the lower and upper limits of any class. Let's calculate it using the first class (1.0-7.9 hours):

• Upper limit = 7.9
• Lower limit = 1.0

Class Width = Upper limit - Lower limit = 7.9 - 1.0 = 6.9 hours

Step 2: Calculate the percentage of students playing video games for less than 15 hours per week

To find the percentage of students playing for less than 15 hours per week, we need to sum the frequencies of the classes that fall below this threshold:

• 1.0-7.9 hours: 26 students
• 8.0-14.9 hours: 40 students

Total Frequency for less than 15 hours = 26 + 40 = 66

Now, to find the percentage, we calculate:

\[ \text{Percentage} = \left( \frac{\text{Total Frequency for less than 15 hours}}{\text{Total Number of Students}} \right) \times 100 \]

\[ \text{Percentage} = \left( \frac{66}{200} \right) \times 100 = 33% \]

Step 3: Calculate the percentage of students playing video games for 8 or more hours per week

To find the percentage of students playing for 8 or more hours, we can sum the frequencies of all classes excluding the first one:

• 8.0-14.9 hours: 40 students
• 15.0-21.9 hours: 48 students
• 22.0-28.9 hours: 25 students
• 29.0-35.9 hours: 20 students
• 36.0-42.9 hours: 15 students
• 43.0-49.9 hours: 10 students
• 50.0-56.9 hours: 5 students
• 57.0-63.9 hours: 3 students
• 64.0-70.9 hours: 8 students

Total Frequency for 8.0 hours or more = 40 + 48 + 25 + 20 + 15 + 10 + 5 + 3 + 8 = 174

Now, we calculate the percentage:

\[ \text{Percentage} = \left( \frac{\text{Total Frequency for 8 or more hours}}{\text{Total Number of Students}} \right) \times 100 \]

\[ \text{Percentage} = \left( \frac{174}{200} \right) \times 100 = 87% \]

Summary:

• Number of Classes: 10
• Class Width: 6.9 hours
• Percentage of students playing for less than 15 hours per week: 33%
• Percentage of students playing for 8 or more hours per week: 87%