Math Problem Statement

The histogram shows the hours per week that each person in a class watches television. Based on this histogram, answer the following questions: 1. How many students are in the class? 2. What is the relative frequency of students who watch 1 to 3 hours of TV? 3. What is the relative frequency of students who watch 7 or more hours of TV?

Solution

Based on the uploaded image, here are the answers to each part:

Step 1: Total Number of Students in the Class

From the histogram:

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

Total number of students: 2+9+6+2=192 + 9 + 6 + 2 = 19 So, there are 19 students in the class.

Step 2: Relative Frequency Calculations

The relative frequency is found by dividing the frequency of each category by the total number of students (19).

a. Relative frequency of students who watch 1 to 3 hours of TV

Relative Frequency=2190.105\text{Relative Frequency} = \frac{2}{19} \approx 0.105

b. Relative frequency of students who watch 7 or more hours of TV

For students who watch 7 or more hours, we sum the students in the 7–9 and 10–12 hour intervals: 6+2=86 + 2 = 8 Relative Frequency=8190.421\text{Relative Frequency} = \frac{8}{19} \approx 0.421

Summary of Answers:

  1. Total students in the class: 19
  2. Relative frequency of students who watch 1 to 3 hours of TV: approximately 0.105
  3. Relative frequency of students who watch 7 or more hours of TV: approximately 0.421

Would you like further details or explanations?


Here are five related questions to deepen your understanding:

  1. What is the relative frequency of students who watch 4–6 hours of TV?
  2. How would the relative frequencies change if one more student joined each interval?
  3. What is the cumulative frequency of students who watch up to 6 hours of TV?
  4. How does increasing the total number of students affect individual relative frequencies?
  5. If one more student is added to the 1–3 hours interval, how does that affect the relative frequency for that interval?

Tip: Calculating relative frequency helps understand the proportion of each category within a dataset, useful for probability and comparison across groups.

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Math Problem Analysis

Mathematical Concepts

Statistics
Relative Frequency
Histogram Analysis

Formulas

Relative Frequency = Frequency of Category / Total Frequency

Theorems

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Suitable Grade Level

Grades 7-9