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Relative Frequencies

Grade 11 · Statistics · Worksheet 2

  1. Isabella is analyzing the results of a survey at her school about participation in extracurricular activities. She collected data from 320 students and found that 84 of them participate in at least two extracurricular activities. What is the relative frequency of students who participate in at least two extracurricular activities? Interpret this relative frequency in the context of the school's student body of 1,200 students. Answer: ______________
  2. A Ferris wheel with a diameter of 40 meters completes one full rotation every 2 minutes. The height of a passenger above the ground, in meters, can be modeled by the function h(t) = 20 + 20sin(πt + φ), where t is time in minutes. If a passenger boards at the lowest point, which is 5 meters above the ground, determine the exact value of φ and the time when the passenger first reaches a height of 35 meters during the ride. Answer: ______________
  3. Noah surveyed 255 Grade 11 students about their preferred method of learning mathematics: 102 chose visual aids. Calculate the relative frequency of students who prefer visual aids and interpret what this value means in the context of the survey. Answer: ______________
  4. Charlotte surveyed 220 Grade 11 students about their preferred method of learning mathematics. 77 students indicated they prefer learning through interactive simulations. What is the relative frequency of students who prefer interactive simulations, and what does this value represent in the context of the survey? Answer: ______________
  5. Emma is analyzing the results of a survey on social media usage among high school students. She finds that the relative frequency of students who spend more than 3 hours per day on social media is 0.35. If the school has a total of 750 students, how many students would she expect to spend more than 3 hours per day on social media? Answer: ______________
  6. Emma surveyed 200 Grade 11 students about their preferred method of learning mathematics. 85 students preferred using visual aids. Calculate the relative frequency of students who prefer visual aids and interpret what this value means in the context of the survey. Answer: ______________
  7. In a survey of 161 students, Sophia found that 96 preferred online learning. The relative frequency is 0.596. Interpret this value in context. Answer: ______________
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Answer Key & Explanations

Relative Frequencies · Grade 11 · Worksheet 2

  1. Isabella is analyzing the results of a survey at her school about participation in extracurricular activities. She collected data from 320 students and found that 84 of them participate in at least two extracurricular activities. What is the relative frequency of students who participate in at least two extracurricular activities? Interpret this relative frequency in the context of the school's student body of 1,200 students. Answer: 0.2625 Solution: Identify the number of students with the characteristic: 84 students participate in at least two extracurricular activities. Identify the total sample size: 320 students. Calculate the relative frequency: 84 / 320.
    Full step-by-step solution

    Step 1: Identify the number of students with the characteristic: 84 students participate in at least two extracurricular activities. Step 2: Identify the total sample size: 320 students. Step 3: Calculate the relative frequency: 84 / 320. Step 4: Simplify the fraction: divide numerator and denominator by 4 to get 21/80. Step 5: Convert to decimal: 21/80 = 0.2625. Step 6: Interpret: The relative frequency 0.2625 means that about 26.25% of the students in the sample participate in at least two extracurricular activities. For the entire school of 1,200 students, we would expect approximately 0.2625 * 1200 = 315 students to participate in at least two extracurricular activities, assuming the sample is representative. The answer is 0.2625.

  2. A Ferris wheel with a diameter of 40 meters completes one full rotation every 2 minutes. The height of a passenger above the ground, in meters, can be modeled by the function h(t) = 20 + 20sin(πt + φ), where t is time in minutes. If a passenger boards at the lowest point, which is 5 meters above the ground, determine the exact value of φ and the time when the passenger first reaches a height of 35 meters during the ride. Answer: φ = -π/2, t = 1/3 minutes Solution: In trigonometric modeling, the phase shift φ adjusts the starting position of the periodic function. When a Ferris wheel passenger boards at the lowest point, this corresponds to the minimum value of the sine function.
    Full step-by-step solution

    In trigonometric modeling, the phase shift φ adjusts the starting position of the periodic function. When a Ferris wheel passenger boards at the lowest point, this corresponds to the minimum value of the sine function. The height function represents vertical displacement from the wheel's center, with the sine component describing the circular motion.

  3. Noah surveyed 255 Grade 11 students about their preferred method of learning mathematics: 102 chose visual aids. Calculate the relative frequency of students who prefer visual aids and interpret what this value means in the context of the survey. Answer: 0.4 Solution: Identify the number of students who prefer visual aids: 102. Identify the total number of students surveyed: 255. Calculate the relative frequency: 102 ÷ 255.
    Full step-by-step solution

    Step 1: Identify the number of students who prefer visual aids: 102. Step 2: Identify the total number of students surveyed: 255. Step 3: Calculate the relative frequency: 102 ÷ 255. Step 4: Simplify the fraction: 102/255 = (51 × 2)/(51 × 5) = 2/5. Step 5: Convert to decimal: 2/5 = 0.4. Step 6: Interpretation: The relative frequency of 0.4 means that 40% of the Grade 11 students surveyed prefer visual aids for learning mathematics. In other words, 2 out of every 5 students in this survey chose visual aids as their preferred method.

  4. Charlotte surveyed 220 Grade 11 students about their preferred method of learning mathematics. 77 students indicated they prefer learning through interactive simulations. What is the relative frequency of students who prefer interactive simulations, and what does this value represent in the context of the survey? Answer: 0.35 Solution: Identify the number of students who prefer interactive simulations: 77. Identify the total number of students surveyed: 220. Calculate the relative frequency: 77 ÷ 220.
    Full step-by-step solution

    Step 1: Identify the number of students who prefer interactive simulations: 77. Step 2: Identify the total number of students surveyed: 220. Step 3: Calculate the relative frequency: 77 ÷ 220. Step 4: Perform the division: 77 ÷ 220 = 0.35. Step 5: Interpretation: The relative frequency 0.35 means that 35% of the surveyed Grade 11 students prefer learning mathematics through interactive simulations. It represents the proportion of the total group that has this preference.

  5. Emma is analyzing the results of a survey on social media usage among high school students. She finds that the relative frequency of students who spend more than 3 hours per day on social media is 0.35. If the school has a total of 750 students, how many students would she expect to spend more than 3 hours per day on social media? Answer: 262.5 Solution: Identify the relative frequency of students who spend more than 3 hours per day on social media: 0.35. Identify the total number of students at the school: 750.
    Full step-by-step solution

    Step 1: Identify the relative frequency of students who spend more than 3 hours per day on social media: 0.35. Step 2: Identify the total number of students at the school: 750. Step 3: Multiply the total number of students by the relative frequency to find the expected count: 750 * 0.35. Step 4: Perform the multiplication: 750 * 0.35 = 262.5. Step 5: The expected number of students who spend more than 3 hours per day on social media is 262.5. Since we are dealing with an expected value from a relative frequency, it is acceptable to leave the answer as a decimal. The answer is 262.5.

  6. Emma surveyed 200 Grade 11 students about their preferred method of learning mathematics. 85 students preferred using visual aids. Calculate the relative frequency of students who prefer visual aids and interpret what this value means in the context of the survey. Answer: 0.425 Solution: Identify the number of students who prefer visual aids: 85. Identify the total number of students surveyed: 200. Calculate the relative frequency: 85 ÷ 200.
    Full step-by-step solution

    Step 1: Identify the number of students who prefer visual aids: 85. Step 2: Identify the total number of students surveyed: 200. Step 3: Calculate the relative frequency: 85 ÷ 200. Step 4: Perform the division: 85 ÷ 200 = 0.425. Step 5: Interpret the meaning: This relative frequency of 0.425 means that 42.5% of the surveyed Grade 11 students prefer learning mathematics using visual aids. In other words, for every 100 students in this survey, about 42 or 43 would be expected to prefer visual aids.

  7. In a survey of 161 students, Sophia found that 96 preferred online learning. The relative frequency is 0.596. Interpret this value in context. Answer: Approximately 59.6% of the surveyed students prefer online learning. Solution: The relative frequency is calculated as (number who prefer online learning) / (total surveyed) 96 / 161 = 0.596 This means 59.6% of the 161 surveyed students prefer online learning In context, this indicates that slightly more than half of the students in this survey prefer online learning over…
    Full step-by-step solution

    Step 1: The relative frequency is calculated as (number who prefer online learning) / (total surveyed) Step 2: 96 / 161 = 0.596 Step 3: This means 59.6% of the 161 surveyed students prefer online learning Step 4: In context, this indicates that slightly more than half of the students in this survey prefer online learning over other options.