Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Sampling & Inference

Grade 11 · Statistics · Worksheet 2

  1. Emma is studying smartphone usage patterns at her high school. She stands outside the main entrance and surveys the first 75 students who arrive. If the school has 1500 students total, what percentage of the student population did Emma sample? Answer: ______________
  2. Ava is studying geometric patterns and creates a sequence of nested squares. The largest square has side length 16 cm. Each subsequent square is inscribed by connecting the midpoints of the previous square's sides, creating a smaller rotated square inside. If this process continues infinitely, what is the total area of all the squares combined? Answer: ______________
  3. Sophia is conducting a survey about smartphone usage patterns among high school students. She stands outside the school library and asks every 10th student who enters to complete her survey. Out of 850 students at the school, she collects 72 responses. What percentage of the total student population is represented in Sophia's sample? Answer: ______________
  4. Emma is studying a geometric pattern where circles are arranged in a triangular formation. The first row has 1 circle, the second row has 3 circles, the third row has 5 circles, and this pattern continues with each row having 2 more circles than the previous row. If there are 9 rows total, how many circles are in the entire formation? Answer: ______________
  5. Liam is conducting a survey about high school students' study habits. He stands outside the school library and asks every 5th student who enters about their study time. Out of 1000 students at the school, he surveys 40 students. What percentage of the total student population did Liam survey? Answer: ______________
  6. Noah is conducting a study about smartphone usage patterns at his high school. He stands outside the school library and surveys every 6th student who enters between 3:00 PM and 4:00 PM. Out of the 121 students who visited the library during this time, he surveyed 16 students. Which statement best describes the potential bias in Noah's sampling method?
    • A. The sample is likely representative because it uses systematic sampling.
    • B. The sample is unbiased because it surveys a random selection of students.
    • C. The sample may underrepresent students who have after-school activities.
    • D. The sample may overrepresent students who frequently use the library.
lessonbunny.com

Answer Key & Explanations

Sampling & Inference · Grade 11 · Worksheet 2

  1. Emma is studying smartphone usage patterns at her high school. She stands outside the main entrance and surveys the first 75 students who arrive. If the school has 1500 students total, what percentage of the student population did Emma sample? Answer: 5 Solution: Emma sampled 75 students out of a total population of 1500 students.
    Full step-by-step solution

    Step 1: Emma sampled 75 students out of a total population of 1500 students. Step 2: To find the percentage, divide the sample size by the total population: 75 ÷ 1500 = 0.05 Step 3: Convert the decimal to a percentage by multiplying by 100: 0.05 × 100 = 5% The answer is 5.

  2. Ava is studying geometric patterns and creates a sequence of nested squares. The largest square has side length 16 cm. Each subsequent square is inscribed by connecting the midpoints of the previous square's sides, creating a smaller rotated square inside. If this process continues infinitely, what is the total area of all the squares combined? Answer: 512 Solution: The first square has area = 16 × 16 = 256 cm² When connecting midpoints of a square, the new inscribed square has area exactly half of the original square This creates a geometric series: 256 + 128 + 64 + 32 + ...
    Full step-by-step solution

    Step 1: The first square has area = 16 × 16 = 256 cm² Step 2: When connecting midpoints of a square, the new inscribed square has area exactly half of the original square Step 3: This creates a geometric series: 256 + 128 + 64 + 32 + ... Step 4: The first term a = 256, common ratio r = 1/2 Step 5: Sum of infinite geometric series = a/(1-r) = 256/(1-1/2) = 256/(1/2) = 256 × 2 = 512 Step 6: The total area of all squares is 512 cm²

  3. Sophia is conducting a survey about smartphone usage patterns among high school students. She stands outside the school library and asks every 10th student who enters to complete her survey. Out of 850 students at the school, she collects 72 responses. What percentage of the total student population is represented in Sophia's sample? Answer: 8.47 Solution: Identify the total population size: 850 students Identify the sample size: 72 students Calculate the percentage: (sample size ÷ total population) × 100 (72 ÷ 850) × 100 = 0.0847 × 100 = 8.47% The answer is 8.47.
    Full step-by-step solution

    Step 1: Identify the total population size: 850 students Step 2: Identify the sample size: 72 students Step 3: Calculate the percentage: (sample size ÷ total population) × 100 Step 4: (72 ÷ 850) × 100 = 0.0847 × 100 = 8.47% The answer is 8.47.

  4. Emma is studying a geometric pattern where circles are arranged in a triangular formation. The first row has 1 circle, the second row has 3 circles, the third row has 5 circles, and this pattern continues with each row having 2 more circles than the previous row. If there are 9 rows total, how many circles are in the entire formation? Answer: 81 Solution: Step 1: Identify the sequence of circles per row: 1, 3, 5, 7, 9, 11, 13, 15, 17 Step 2: This is an arithmetic sequence of odd numbers with first term a₁ = 1 and common difference d = 2 Step 3: The sum of the first n odd numbers equals n² Step 4: With n = 9 rows, the total number of circles = 9²…
    Full step-by-step solution

    Step 1: Identify the sequence of circles per row: 1, 3, 5, 7, 9, 11, 13, 15, 17 Step 2: This is an arithmetic sequence of odd numbers with first term a₁ = 1 and common difference d = 2 Step 3: The sum of the first n odd numbers equals n² Step 4: With n = 9 rows, the total number of circles = 9² = 81 Step 5: Verify: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81 The answer is 81.

  5. Liam is conducting a survey about high school students' study habits. He stands outside the school library and asks every 5th student who enters about their study time. Out of 1000 students at the school, he surveys 40 students. What percentage of the total student population did Liam survey? Answer: 4 Solution: Liam surveyed 40 students out of a total population of 1000 students.
    Full step-by-step solution

    Step 1: Liam surveyed 40 students out of a total population of 1000 students. Step 2: To find the percentage, divide the number surveyed by the total population: 40 ÷ 1000 = 0.04 Step 3: Convert the decimal to a percentage by multiplying by 100: 0.04 × 100 = 4% The answer is 4.

  6. Noah is conducting a study about smartphone usage patterns at his high school. He stands outside the school library and surveys every 6th student who enters between 3:00 PM and 4:00 PM. Out of the 121 students who visited the library during this time, he surveyed 16 students. Which statement best describes the potential bias in Noah's sampling method? Answer: D. The sample may overrepresent students who frequently use the library. Solution: When evaluating sampling methods, it's important to consider whether certain groups are systematically included or excluded.
    Full step-by-step solution

    When evaluating sampling methods, it's important to consider whether certain groups are systematically included or excluded. A sample taken only from library visitors during a specific hour might not represent the entire student population's habits. For example, if you surveyed only students in the cafeteria during lunch about exercise habits, you might miss athletes who eat elsewhere. The location and time of sampling can significantly influence which population segments are included.