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Relative Frequencies

Grade 11 · Statistics · Worksheet 1

  1. Noah surveyed 220 Grade 11 students about their preferred method of study. 143 students indicated they prefer studying in groups. What is the relative frequency of students who prefer group study, and what does this value mean in the context of the survey? Answer: ______________
  2. Kaia surveyed 231 Grade 11 students about their preferred method of studying for exams. 77 students preferred group study sessions. What is the relative frequency of students who prefer group study, and what does this value mean in context? Answer: ______________
  3. A marine biologist is studying the population dynamics of a dolphin pod. She observes that the relative frequency of juvenile dolphins in the pod is 0.28. If the total pod size is 75 dolphins, and the biologist wants to estimate how many dolphins would be juveniles in a larger population of 500 dolphins from the same ecosystem, what is her best estimate based on this relative frequency? Answer: ______________
  4. In a survey of 143 students, 77 preferred online learning. The relative frequency of students who prefer online learning is approximately 0.538. Interpret this relative frequency in the context of the survey. Answer: ______________
  5. Isabella is analyzing a two-way table from a survey of 427 Grade 11 students about their participation in extracurricular activities. The table shows that 187 students participate in sports and 112 of those sports participants also play a musical instrument. The relative frequency of students who play a musical instrument among sports participants is 112/187. In the context of this survey, what does the relative frequency 112/187 represent? Answer: ______________
  6. Liam is analyzing data from a local library to understand reading habits. He finds that out of 450 library members surveyed, 180 members borrowed at least one non-fiction book last month. Based on this relative frequency, if the library has 5,000 members total, how many members would be expected to borrow at least one non-fiction book in a given month? Answer: ______________
  7. A city's public health department is tracking the spread of a new virus strain. In a sample of 1200 residents, 450 tested positive. The department wants to estimate the probability that a resident chosen at random from the city is infected. Based on this sample, what is the relative frequency probability of infection? Express your answer as a decimal rounded to three decimal places. Answer: ______________
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Answer Key & Explanations

Relative Frequencies · Grade 11 · Worksheet 1

  1. Noah surveyed 220 Grade 11 students about their preferred method of study. 143 students indicated they prefer studying in groups. What is the relative frequency of students who prefer group study, and what does this value mean in the context of the survey? Answer: 0.65 Solution: Identify the number of students who prefer group study: 143 Identify the total number of students surveyed: 220 Calculate the relative frequency: 143 ÷ 220 Perform the division: 143 ÷ 220 = 0.65 Interpretation: The relative frequency 0.65 means that 65% of the surveyed Grade 11 students prefer…
    Full step-by-step solution

    Step 1: Identify the number of students who prefer group study: 143 Step 2: Identify the total number of students surveyed: 220 Step 3: Calculate the relative frequency: 143 ÷ 220 Step 4: Perform the division: 143 ÷ 220 = 0.65 Step 5: Interpretation: The relative frequency 0.65 means that 65% of the surveyed Grade 11 students prefer studying in groups. This represents the proportion of the sample that has this preference, and it can be interpreted as the probability that a randomly selected student from this group prefers group study.

  2. Kaia surveyed 231 Grade 11 students about their preferred method of studying for exams. 77 students preferred group study sessions. What is the relative frequency of students who prefer group study, and what does this value mean in context? Answer: 0.333... or 1/3 Solution: Identify the number of students who prefer group study: 77. Identify the total number of students surveyed: 231. Calculate the relative frequency: 77 ÷ 231.
    Full step-by-step solution

    Step 1: Identify the number of students who prefer group study: 77. Step 2: Identify the total number of students surveyed: 231. Step 3: Calculate the relative frequency: 77 ÷ 231. Step 4: Simplify the fraction: 77/231 = (77 ÷ 77) / (231 ÷ 77) = 1/3. Step 5: As a decimal, 1/3 = 0.333... (repeating). Interpretation: This means that approximately 33.3% of the surveyed students prefer group study sessions, or 1 out of every 3 students in this group prefers this method.

  3. A marine biologist is studying the population dynamics of a dolphin pod. She observes that the relative frequency of juvenile dolphins in the pod is 0.28. If the total pod size is 75 dolphins, and the biologist wants to estimate how many dolphins would be juveniles in a larger population of 500 dolphins from the same ecosystem, what is her best estimate based on this relative frequency? Answer: 140 Solution: The observed relative frequency of juvenile dolphins is 0.28 This relative frequency represents the proportion of juveniles in the population For the larger population of 500 dolphins, multiply the total population by the relative frequency: 500 × 0.28 500 × 0.28 = 140 The best estimate for the…
    Full step-by-step solution

    Step 1: The observed relative frequency of juvenile dolphins is 0.28 Step 2: This relative frequency represents the proportion of juveniles in the population Step 3: For the larger population of 500 dolphins, multiply the total population by the relative frequency: 500 × 0.28 Step 4: 500 × 0.28 = 140 Step 5: The best estimate for the number of juvenile dolphins in the larger population is 140

  4. In a survey of 143 students, 77 preferred online learning. The relative frequency of students who prefer online learning is approximately 0.538. Interpret this relative frequency in the context of the survey. Answer: Approximately 53.8% of the surveyed students prefer online learning Solution: The relative frequency is calculated as the number of students who prefer online learning divided by the total number of students surveyed. 77 students prefer online learning out of 143 total students.
    Full step-by-step solution

    Step 1: The relative frequency is calculated as the number of students who prefer online learning divided by the total number of students surveyed. Step 2: 77 students prefer online learning out of 143 total students. Step 3: The relative frequency of 0.538 means that for every student in the survey, there is a 0.538 probability that they prefer online learning. Step 4: In percentage terms, this means approximately 53.8% of the surveyed students prefer online learning. Step 5: Therefore, the interpretation is that slightly more than half of the students in this survey prefer online learning.

  5. Isabella is analyzing a two-way table from a survey of 427 Grade 11 students about their participation in extracurricular activities. The table shows that 187 students participate in sports and 112 of those sports participants also play a musical instrument. The relative frequency of students who play a musical instrument among sports participants is 112/187. In the context of this survey, what does the relative frequency 112/187 represent? Answer: The proportion of sports participants who also play a musical instrument. Solution: Identify the total number of sports participants: 187 students. Identify the number of sports participants who also play a musical instrument: 112 students.
    Full step-by-step solution

    Step 1: Identify the total number of sports participants: 187 students. Step 2: Identify the number of sports participants who also play a musical instrument: 112 students. Step 3: The relative frequency is calculated as (number in the subgroup) / (total in the group of interest). Here, the subgroup is sports participants who play an instrument, and the group of interest is all sports participants. Step 4: Therefore, 112/187 represents the proportion (or fraction) of sports participants who also play a musical instrument. Final Answer: The proportion of sports participants who also play a musical instrument.

  6. Liam is analyzing data from a local library to understand reading habits. He finds that out of 450 library members surveyed, 180 members borrowed at least one non-fiction book last month. Based on this relative frequency, if the library has 5,000 members total, how many members would be expected to borrow at least one non-fiction book in a given month? Answer: 2000 Solution: Calculate the relative frequency of members who borrowed non-fiction books from the sample. Relative frequency = Number of members who borrowed non-fiction / Total sample size = 180 / 450.
    Full step-by-step solution

    Step 1: Calculate the relative frequency of members who borrowed non-fiction books from the sample. Relative frequency = Number of members who borrowed non-fiction / Total sample size = 180 / 450. Step 2: Simplify the fraction: 180/450 = 18/45 = 2/5 = 0.4. Step 3: Apply this relative frequency to the total library membership. Expected number = Relative frequency × Total members = 0.4 × 5000. Step 4: Perform the multiplication: 0.4 × 5000 = 2000. The answer is 2000.

  7. A city's public health department is tracking the spread of a new virus strain. In a sample of 1200 residents, 450 tested positive. The department wants to estimate the probability that a resident chosen at random from the city is infected. Based on this sample, what is the relative frequency probability of infection? Express your answer as a decimal rounded to three decimal places. Answer: 0.375 Solution: We are given a sample of 1200 residents, and 450 tested positive. We want the relative frequency probability of infection.
    Full step-by-step solution

    Step 1: Understand the problem We are given a sample of 1200 residents, and 450 tested positive. We want the relative frequency probability of infection. Relative frequency probability = (Number of times event occurs) / (Total number of trials or observations). Step 2: Identify the numbers Number of positive cases = 450 Total sample size = 1200 Step 3: Write the relative frequency formula Probability = (Number of positive cases) / (Total residents in sample) Probability = 450 / 1200 Step 4: Simplify the fraction Both numerator and denominator can be divided by 150: 450 ÷ 150 = 3 1200 ÷ 150 = 8 So, 450/1200 = 3/8 Step 5: Convert to decimal 3 divided by 8 = 0.375 Step 6: Round to three decimal places 0.375 is already to three decimal places. Final Answer: 0.375