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Relative Frequencies

Grade 11 · Statistics · Worksheet 1

  1. Mere is analyzing data from a regional survey on sustainable farming practices. The survey of 240 farms found that 156 farms use organic composting. Based on this relative frequency, if the region has 4,800 farms in total, how many farms would be expected to use organic composting? Interpret the relative frequency in context. Answer: ______________
  2. In a survey of 180 students, Hana found that 54 students prefer online learning. What is the relative frequency of students who prefer online learning, and what does this value mean in context? Answer: ______________
  3. Hana is analyzing the data from a survey of 240 students at her school about their preferred method of learning mathematics. The survey found that 84 students prefer learning through interactive digital platforms. Based on this relative frequency, if the entire school has 1,200 students, how many students would Hana expect to prefer interactive digital platforms? Answer: ______________
  4. A biologist is studying the growth of a bacterial culture and models the population using the function P(t) = 500e^(0.03t), where t is time in hours. After collecting data for 24 hours, she notices the actual growth follows a slightly different pattern. She calculates the relative frequency of the model's prediction being within 5% of the actual count across 20 measurements. If 15 of these measurements fell within this 5% margin, what is the relative frequency of the model's predictions being accurate within 5%? Answer: ______________
  5. Charlotte surveyed 272 Grade 11 students about their preferred method of learning mathematics. 187 students indicated they prefer collaborative group work. Calculate the relative frequency of students who prefer collaborative group work and interpret what this value means in the context of the survey. Answer: ______________
  6. Aroha is analyzing data from a local sports centre. She records the preferred sport of 450 teenagers and finds that 117 prefer basketball. What is the relative frequency of teenagers who prefer basketball in this sample? Interpret this relative frequency in the context of the sports centre's programming decisions. Answer: ______________
  7. 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: ______________
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Answer Key & Explanations

Relative Frequencies · Grade 11 · Worksheet 1

  1. Mere is analyzing data from a regional survey on sustainable farming practices. The survey of 240 farms found that 156 farms use organic composting. Based on this relative frequency, if the region has 4,800 farms in total, how many farms would be expected to use organic composting? Interpret the relative frequency in context. Answer: 3120 Solution: Calculate the relative frequency of farms using organic composting in the sample. Relative frequency = Number of farms using composting / Total sample size = 156 / 240.
    Full step-by-step solution

    Step 1: Calculate the relative frequency of farms using organic composting in the sample. Relative frequency = Number of farms using composting / Total sample size = 156 / 240. Step 2: Simplify the fraction: 156 / 240 = 13 / 20 = 0.65. This means that in the sample, 65% of farms use organic composting. Step 3: Apply this relative frequency to the larger population of 4,800 farms. Expected number = Relative frequency × Total population = 0.65 × 4800. Step 4: Perform the calculation: 0.65 × 4800 = 3120. Therefore, based on the sample data, we would expect 3,120 farms in the region to use organic composting.

  2. In a survey of 180 students, Hana found that 54 students prefer online learning. What is the relative frequency of students who prefer online learning, and what does this value mean in context? Answer: 0.3 Solution: Identify the number of students who prefer online learning: 54 Identify the total number of students surveyed: 180 Calculate the relative frequency: 54 ÷ 180 = 0.3 Interpret the meaning: A relative frequency of 0.3 means that 30% of the surveyed students prefer online learning, or that the…
    Full step-by-step solution

    Step 1: Identify the number of students who prefer online learning: 54 Step 2: Identify the total number of students surveyed: 180 Step 3: Calculate the relative frequency: 54 ÷ 180 = 0.3 Step 4: Interpret the meaning: A relative frequency of 0.3 means that 30% of the surveyed students prefer online learning, or that the proportion of students who prefer online learning in this sample is 0.3.

  3. Hana is analyzing the data from a survey of 240 students at her school about their preferred method of learning mathematics. The survey found that 84 students prefer learning through interactive digital platforms. Based on this relative frequency, if the entire school has 1,200 students, how many students would Hana expect to prefer interactive digital platforms? Answer: 420 Solution: Calculate the relative frequency from the sample data. Relative frequency = Number of students preferring digital platforms / Total sample size Relative frequency = 84 / 240 Simplify the fraction.
    Full step-by-step solution

    Step 1: Calculate the relative frequency from the sample data. Relative frequency = Number of students preferring digital platforms / Total sample size Relative frequency = 84 / 240 Step 2: Simplify the fraction. 84 / 240 = 7 / 20 (divide numerator and denominator by 12) Step 3: Apply this relative frequency to the entire school population. Expected number = Relative frequency × Total school population Expected number = (7/20) × 1200 Step 4: Perform the calculation. (7/20) × 1200 = 7 × (1200 / 20) = 7 × 60 = 420 Step 5: The expected number of students who prefer interactive digital platforms is 420.

  4. A biologist is studying the growth of a bacterial culture and models the population using the function P(t) = 500e^(0.03t), where t is time in hours. After collecting data for 24 hours, she notices the actual growth follows a slightly different pattern. She calculates the relative frequency of the model's prediction being within 5% of the actual count across 20 measurements. If 15 of these measurements fell within this 5% margin, what is the relative frequency of the model's predictions being accurate within 5%? Answer: 0.75 Solution: The function \( P(t) = 500 e^{0.03t} \) is the model, but the actual data is slightly different. The biologist collected 20 measurements over 24 hours.
    Full step-by-step solution

    Let's go step by step. --- **Step 1: Understanding the problem** The function \( P(t) = 500 e^{0.03t} \) is the model, but the actual data is slightly different. The biologist collected 20 measurements over 24 hours. She checks how often the model's prediction is within 5% of the actual count. She found that 15 of the 20 measurements were within this 5% margin. We are asked for the **relative frequency** of the model's predictions being accurate within 5%. --- **Step 2: Recall relative frequency formula** Relative frequency = (Number of successful outcomes) / (Total number of trials) Here: - Successful outcomes = measurements within 5% margin = 15 - Total measurements = 20 --- **Step 3: Calculate relative frequency** Relative frequency = 15 / 20 --- **Step 4: Simplify** 15 / 20 = 3 / 4 = 0.75 --- **Step 5: Interpret the result** The relative frequency of the model being within 5% of the actual count is 0.75. --- **Final Answer:** 0.75

  5. Charlotte surveyed 272 Grade 11 students about their preferred method of learning mathematics. 187 students indicated they prefer collaborative group work. Calculate the relative frequency of students who prefer collaborative group work and interpret what this value means in the context of the survey. Answer: 0.6875 Solution: Identify the number of students who prefer collaborative group work: 187. Identify the total number of students surveyed: 272. Calculate the relative frequency: 187 ÷ 272.
    Full step-by-step solution

    Step 1: Identify the number of students who prefer collaborative group work: 187. Step 2: Identify the total number of students surveyed: 272. Step 3: Calculate the relative frequency: 187 ÷ 272. Step 4: Perform the division: 187 ÷ 272 = 0.6875. Step 5: Interpretation: The relative frequency 0.6875 means that approximately 68.75% of the Grade 11 students surveyed prefer collaborative group work for learning mathematics. In other words, about 687 out of every 1000 students in this population would be expected to prefer this method.

  6. Aroha is analyzing data from a local sports centre. She records the preferred sport of 450 teenagers and finds that 117 prefer basketball. What is the relative frequency of teenagers who prefer basketball in this sample? Interpret this relative frequency in the context of the sports centre's programming decisions. Answer: 0.26 Solution: Identify the number of teenagers who prefer basketball: 117. Identify the total number of teenagers in the sample: 450. Relative frequency = (number preferring basketball) / (total number) = 117 / 450.
    Full step-by-step solution

    Step 1: Identify the number of teenagers who prefer basketball: 117. Step 2: Identify the total number of teenagers in the sample: 450. Step 3: Relative frequency = (number preferring basketball) / (total number) = 117 / 450. Step 4: Simplify the fraction: divide numerator and denominator by 9 to get 13 / 50, or divide directly: 117 / 450 = 0.26. Step 5: Interpretation: The relative frequency of 0.26 means that 26% of the teenagers in the sample prefer basketball. For the sports centre, this suggests that about 26 out of every 100 teenagers are likely to be interested in basketball, which could guide decisions on allocating court space, scheduling basketball programs, or ordering equipment. The answer is 0.26.

  7. 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.