Math Problem Statement

The histogram shows the hours per week each person in a class watches television. Determine the total number of students in the class, the relative frequency of students who watch 4-6 hours of TV, and the relative frequency of students who watch 4 or more hours of TV.

Solution

From the histogram:

  1. Finding the total number of students in the class:

    • 1–3 hours: Frequency = 2
    • 4–6 hours: Frequency = 10
    • 7–9 hours: Frequency = 6
    • 10–12 hours: Frequency = 2

    Total number of students = 2+10+6+2=202 + 10 + 6 + 2 = 20 students.

  2. Relative frequency of students who watch 4–6 hours of TV:

    • Relative frequency = Frequency for 4–6 hoursTotal students\frac{\text{Frequency for 4–6 hours}}{\text{Total students}}
    • 1020=0.5\frac{10}{20} = 0.5 or 50%.
  3. Relative frequency of students who watch 4 or more hours of TV:

    • Add frequencies for 4–6, 7–9, and 10–12 hours: 10+6+2=1810 + 6 + 2 = 18.
    • Relative frequency = 1820=0.9\frac{18}{20} = 0.9 or 90%.

Final Answers:

  1. Total students in the class: 20 students.
  2. Relative frequency (4–6 hours): 0.5 or 50%.
  3. Relative frequency (4 or more hours): 0.9 or 90%.

Would you like a breakdown of how relative frequency is calculated or any other details?

Here are 5 related questions you might find useful:

  1. How do you calculate cumulative frequency from a histogram?
  2. What is the significance of relative frequency in statistics?
  3. How do you represent relative frequency on a histogram?
  4. What is the difference between relative and absolute frequency?
  5. Can relative frequencies sum to more than 1? Why or why not?

Tip: Always ensure that the total relative frequency sums to 1 to confirm the calculation accuracy.

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Math Problem Analysis

Mathematical Concepts

Frequency Distribution
Relative Frequency
Histogram Analysis

Formulas

Relative Frequency = (Frequency of the Interval) / (Total Frequency)
Total Frequency = Sum of all interval frequencies

Theorems

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Suitable Grade Level

Grades 6-8