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

number of hours and frequency:
1.0 - 7.9 at 30
8.0-14.9 at 33
15.0-21.9 at 43
22.0-28.9 at 25
29.0-35.9 at 21
36-42.9 at 17
43.0-49.9 at 10
50.0-56.9 at 6
57.0-63.9 at 3
64.0-70.9 at 12

how many classes are there?
what is the class width?

Answer 1

To determine the number of classes and the class width from the given frequency distribution, we can analyze the data.

1. Number of Classes: The number of classes can be counted from the provided frequency distribution intervals:

   • 1.0 - 7.9
   • 8.0 - 14.9
   • 15.0 - 21.9
   • 22.0 - 28.9
   • 29.0 - 35.9
   • 36.0 - 42.9
   • 43.0 - 49.9
   • 50.0 - 56.9
   • 57.0 - 63.9
   • 64.0 - 70.9

   There are 10 classes in total.

2. Class Width: To find the class width, we can subtract the lower boundary of one class from the lower boundary of the next class. For example, using the first and second classes:

   • Lower boundary of the first class = 1.0
   • Lower boundary of the second class = 8.0

   Class width = 8.0 - 1.0 = 7.0

Alternatively, we might also find the class width by taking the upper boundary of the first class and the lower boundary of the second class:

• Upper boundary of the first class = 7.9
• Lower boundary of the second class = 8.0

Class width = 8.0 - 1.0 = 7.0 (which confirms our previous calculation).

Thus, the class width is 7.0 hours.

In summary:

• Number of classes: 10
• Class width: 7.0 hours.

Answer 2

Do not round.

(c) What percentage of students play video games for less than 57 hr per week?

D) what percentage plays 50 or more hours per week?

Answer 3

To calculate the percentages of students who play video games for less than 57 hours and those who play 50 or more hours per week, we can use the frequency distribution provided.

Given Frequency Distribution:

• 1.0 - 7.9: 30
• 8.0 - 14.9: 33
• 15.0 - 21.9: 43
• 22.0 - 28.9: 25
• 29.0 - 35.9: 21
• 36.0 - 42.9: 17
• 43.0 - 49.9: 10
• 50.0 - 56.9: 6
• 57.0 - 63.9: 3
• 64.0 - 70.9: 12

Total number of students surveyed:

200

(c) Percentage of students playing less than 57 hours per week:

To find this, we sum the frequencies of all classes below 57 hours.

• Classes below 57 hours:
  • 1.0 - 7.9: 30
  • 8.0 - 14.9: 33
  • 15.0 - 21.9: 43
  • 22.0 - 28.9: 25
  • 29.0 - 35.9: 21
  • 36.0 - 42.9: 17
  • 43.0 - 49.9: 10
  • 50.0 - 56.9: 6
  • Total = 30 + 33 + 43 + 25 + 21 + 17 + 10 + 6 + 3 = 288 = 30 + 33 + 43 + 25 + 21 + 17 + 10 + 6

Total playing less than 57 hours = 30 + 33 + 43 + 25 + 21 + 17 + 10 + 6 + 3 = 288

Now calculate the percentage: \[ \text{Percentage} = \left( \frac{\text{Total less than 57 hours}}{\text{Total number of students}} \right) \times 100 \] \[ = \left( \frac{194}{200} \right) \times 100 = 97% \]

(d) Percentage of students playing 50 or more hours per week:

To find this, we sum the frequencies of classes that are at or above 50 hours.

• Classes for 50 or more hours:
  • 50.0 - 56.9: 6
  • 57.0 - 63.9: 3
  • 64.0 - 70.9: 12
  • Total = 6 + 3 + 12 = 21

Now calculate the percentage: \[ \text{Percentage} = \left( \frac{\text{Total 50 or more hours}}{\text{Total number of students}} \right) \times 100 \] \[ = \left( \frac{21}{200} \right) \times 100 = 10.5% \]

Summary:

• (c) Percentage of students playing video games for less than 57 hours per week: 97%
• (d) Percentage of students playing 50 or more hours per week: 10.5%