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Population Comparison

Grade 7 · Statistics · Worksheet 3

  1. Liam and Olivia each recorded the number of minutes they spent reading each day for 10 days. The double box plot below shows their data. Liam's data has a minimum of 15, first quartile of 30, median of 45, third quartile of 60, and maximum of 75. Olivia's data has a minimum of 20, first quartile of 35, median of 50, third quartile of 65, and maximum of 80. Compare the two data sets by describing the differences in their medians and interquartile ranges (IQR). Answer: ______________
  2. (-3)² × 2 - 4 × (-5) + 12 ÷ (-3) = ? Answer: ______________
  3. A city is comparing the average daily ridership of two public transportation systems. The bus system had an average of 12,450 riders per day last month, while the light rail system had an average of 8,760 riders per day. If the bus system operated for 28 days and the light rail system operated for 31 days, which transportation system had more total riders for the month, and by how many? Answer: ______________
  4. Population A: mean = 68, median = 66, range = 24. Population B: mean = 74, median = 76, range = 18. Compare the centers and variabilities of the two populations. Answer: ______________
  5. Hana is comparing the annual book sales of two bookstores in her city. Bookstore A had an average of 15,600 books sold per month last year, while Bookstore B had an average of 11,400 books sold per month. If Bookstore A operated for all 12 months, but Bookstore B was closed for renovations in January and February (so it only operated for 10 months), which bookstore sold more books in total last year, and by how many? Answer: ______________
  6. Liam is comparing the test scores of his two math classes. Class A has 28 students with a mean score of 82. Class B has 32 students with a mean score of 78. What is the combined mean score for both classes? Answer: ______________
  7. (-3)² × 4 - 18 ÷ (2 + 1) = ? Answer: ______________
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Answer Key & Explanations

Population Comparison · Grade 7 · Worksheet 3

  1. Liam and Olivia each recorded the number of minutes they spent reading each day for 10 days. The double box plot below shows their data. Liam's data has a minimum of 15, first quartile of 30, median of 45, third quartile of 60, and maximum of 75. Olivia's data has a minimum of 20, first quartile of 35, median of 50, third quartile of 65, and maximum of 80. Compare the two data sets by describing the differences in their medians and interquartile ranges (IQR). Answer: Liam's median is 45, Olivia's median is 50; Olivia's median is 5 minutes higher. Liam's IQR is 30, Olivia's IQR is 30; the IQRs are equal. Solution: Identify the median for Liam. The median is 45 minutes. Step 2: Identify the median for Olivia.
    Full step-by-step solution

    Step 1: Identify the median for Liam. The median is 45 minutes. Step 2: Identify the median for Olivia. The median is 50 minutes. Step 3: Compare medians: 50 - 45 = 5, so Olivia's median is 5 minutes higher. Step 4: Calculate Liam's IQR: third quartile (60) minus first quartile (30) = 30. Step 5: Calculate Olivia's IQR: third quartile (65) minus first quartile (35) = 30. Step 6: Compare IQRs: both are 30, so the variability in reading time is the same for both. Final answer: Liam's median is 45, Olivia's median is 50; Olivia's median is 5 minutes higher. Liam's IQR is 30, Olivia's IQR is 30; the IQRs are equal.

  2. (-3)² × 2 - 4 × (-5) + 12 ÷ (-3) = ? Answer: 34 Solution: Evaluate the exponent: (-3)² = 9 Perform multiplications and divisions from left to right: 9 × 2 = 18, 4 × (-5) = -20, 12 ÷ (-3) = -4 Rewrite the expression with these results: 18 - (-20) + (-4) Simplify the subtraction of a negative: 18 + 20 + (-4) Add from left to right: 18 + 20 = 38, 38 +…
    Full step-by-step solution

    Step 1: Evaluate the exponent: (-3)² = 9 Step 2: Perform multiplications and divisions from left to right: 9 × 2 = 18, 4 × (-5) = -20, 12 ÷ (-3) = -4 Step 3: Rewrite the expression with these results: 18 - (-20) + (-4) Step 4: Simplify the subtraction of a negative: 18 + 20 + (-4) Step 5: Add from left to right: 18 + 20 = 38, 38 + (-4) = 34 The answer is 34.

  3. A city is comparing the average daily ridership of two public transportation systems. The bus system had an average of 12,450 riders per day last month, while the light rail system had an average of 8,760 riders per day. If the bus system operated for 28 days and the light rail system operated for 31 days, which transportation system had more total riders for the month, and by how many? Answer: The bus system had 23,820 more total riders Solution: Bus system: 12,450 riders/day × 28 days = 348,600 total riders Light rail system: 8,760 riders/day × 31 days = 271,560 total riders 348,600 (bus) - 271,560 (light rail) = 77,040 more riders on the bus system The bus system had 348,600 riders and the light rail system had 271,560 riders, so the…
    Full step-by-step solution

    Step 1: Calculate total bus riders Bus system: 12,450 riders/day × 28 days = 348,600 total riders Step 2: Calculate total light rail riders Light rail system: 8,760 riders/day × 31 days = 271,560 total riders Step 3: Compare the totals 348,600 (bus) - 271,560 (light rail) = 77,040 more riders on the bus system Step 4: Determine which system had more The bus system had 348,600 riders and the light rail system had 271,560 riders, so the bus system had more total riders. Step 5: Calculate the difference 348,600 - 271,560 = 77,040 The bus system had 77,040 more total riders than the light rail system.

  4. Population A: mean = 68, median = 66, range = 24. Population B: mean = 74, median = 76, range = 18. Compare the centers and variabilities of the two populations. Answer: Population B has a higher center (mean 74 vs 68, median 76 vs 66) and less variability (range 18 vs 24) than Population A. Solution: Compare the means. Population A mean = 68, Population B mean = 74. Since 74 > 68, Population B has a higher average value.
    Full step-by-step solution

    Step 1: Compare the means. Population A mean = 68, Population B mean = 74. Since 74 > 68, Population B has a higher average value. Step 2: Compare the medians. Population A median = 66, Population B median = 76. Since 76 > 66, Population B also has a higher middle value. Step 3: Compare the ranges. Population A range = 24, Population B range = 18. Since 18 < 24, Population B has less spread or variability in its data. Step 4: Conclusion. Population B has a higher center (both mean and median are larger) and less variability (smaller range) than Population A.

  5. Hana is comparing the annual book sales of two bookstores in her city. Bookstore A had an average of 15,600 books sold per month last year, while Bookstore B had an average of 11,400 books sold per month. If Bookstore A operated for all 12 months, but Bookstore B was closed for renovations in January and February (so it only operated for 10 months), which bookstore sold more books in total last year, and by how many? Answer: Bookstore A sold 73,200 more books than Bookstore B Solution: Calculate total books sold by Bookstore A. Bookstore A: 15,600 books per month x 12 months = 187,200 books Calculate total books sold by Bookstore B. Bookstore B operated for 12 - 2 = 10 months.
    Full step-by-step solution

    Step 1: Calculate total books sold by Bookstore A. Bookstore A: 15,600 books per month x 12 months = 187,200 books Step 2: Calculate total books sold by Bookstore B. Bookstore B operated for 12 - 2 = 10 months. Bookstore B: 11,400 books per month x 10 months = 114,000 books Step 3: Compare the totals. 187,200 (Bookstore A) - 114,000 (Bookstore B) = 73,200 more books sold by Bookstore A. Step 4: State the result. Bookstore A sold 73,200 more books than Bookstore B.

  6. Liam is comparing the test scores of his two math classes. Class A has 28 students with a mean score of 82. Class B has 32 students with a mean score of 78. What is the combined mean score for both classes? Answer: 79.87 Solution: To find the combined mean score for both classes, we need to calculate the total sum of all test scores from both classes and then divide by the total number of students. Calculate the total sum of scores for Class A. We know the mean score for Class A is 82, and there are 28 students.
    Full step-by-step solution

    To find the combined mean score for both classes, we need to calculate the total sum of all test scores from both classes and then divide by the total number of students. Step 1: Calculate the total sum of scores for Class A. We know the mean score for Class A is 82, and there are 28 students. The total sum for Class A = mean × number of students = 82 × 28. Let's calculate that: 82 × 28 = 82 × (20 + 8) = (82 × 20) + (82 × 8) = 1640 + 656 = 2296. So, the total score for Class A is 2296. Step 2: Calculate the total sum of scores for Class B. We know the mean score for Class B is 78, and there are 32 students. The total sum for Class B = mean × number of students = 78 × 32. Let's calculate that: 78 × 32 = 78 × (30 + 2) = (78 × 30) + (78 × 2) = 2340 + 156 = 2496. So, the total score for Class B is 2496. Step 3: Calculate the overall total sum of scores and the total number of students. Overall total score = Class A total + Class B total = 2296 + 2496 = 4792. Total number of students = 28 + 32 = 60. Step 4: Calculate the combined mean score. The combined mean is the overall total score divided by the total number of students. Combined mean = 4792 / 60. Step 5: Perform the division to find the mean. Let's calculate 4792 ÷ 60. First, 60 × 79 = 60 × (80 - 1) = (60 × 80) - (60 × 1) = 4800 - 60 = 4740. Now, subtract this from 4792: 4792 - 4740 = 52. So, 4792 / 60 = 79 + 52/60. Simplify the fraction 52/60 by dividing numerator and denominator by 4: (52 ÷ 4) / (60 ÷ 4) = 13/15. Therefore, 4792 / 60 = 79 + 13/15. Step 6: Convert the fractional part to a decimal. 13/15 as a decimal is approximately 0.8666... So, 79 + 0.8666... = 79.8666..., which rounds to 79.87. Thus, the combined mean score for both classes is 79.87.

  7. (-3)² × 4 - 18 ÷ (2 + 1) = ? Answer: 30 Solution: Solve inside the parentheses: (2 + 1) = 3. The expression becomes (-3)² × 4 - 18 ÷ 3. Evaluate the exponent: (-3)² = 9.
    Full step-by-step solution

    Step 1: Solve inside the parentheses: (2 + 1) = 3. The expression becomes (-3)² × 4 - 18 ÷ 3. Step 2: Evaluate the exponent: (-3)² = 9. The expression becomes 9 × 4 - 18 ÷ 3. Step 3: Perform multiplication and division from left to right: 9 × 4 = 36, and 18 ÷ 3 = 6. The expression becomes 36 - 6. Step 4: Perform the subtraction: 36 - 6 = 30. The final answer is 30.