Data Interpretation

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Data Interpretation · Grade 6 · Worksheet 2

1. A school is planning a field trip to the science museum. There are 240 students going on the trip, and the museum requires one adult chaperone for every 12 students. If each school bus can carry 48 people (students and adults combined), how many buses are needed for the trip? Answer: 6 Solution: Calculate the number of adult chaperones needed. There are 240 students and 1 chaperone per 12 students. 240 ÷ 12 = 20 chaperones Calculate the total number of people going on the trip.
   Full step-by-step solution

   Step 1: Calculate the number of adult chaperones needed. There are 240 students and 1 chaperone per 12 students. 240 ÷ 12 = 20 chaperones Step 2: Calculate the total number of people going on the trip. Students: 240 Chaperones: 20 Total people: 240 + 20 = 260 Step 3: Calculate how many buses are needed. Each bus carries 48 people. 260 ÷ 48 = 5.4166... Since we can't have a fraction of a bus, we need to round up to the next whole number. 6 buses are needed. The answer is 6 buses.

2. A rectangular prism is drawn on a coordinate grid with vertices at (0,0,0), (8,0,0), (8,5,0), (0,5,0), (0,0,4), (8,0,4), (8,5,4), and (0,5,4). If you draw all the space diagonals of this prism (lines connecting vertices that are not on the same face), how many distinct space diagonals are there? Answer: 4 Solution: A rectangular prism has 8 vertices total. Space diagonals connect vertices that are not on the same face. This means they connect vertices that are not sharing an edge or face.
   Full step-by-step solution

   Step 1: A rectangular prism has 8 vertices total. Step 2: Space diagonals connect vertices that are not on the same face. This means they connect vertices that are not sharing an edge or face. Step 3: Each vertex can connect to exactly one other vertex with a space diagonal (the vertex directly opposite through the center of the prism). Step 4: For vertex (0,0,0), the space diagonal goes to (8,5,4). Step 5: For vertex (8,0,0), the space diagonal goes to (0,5,4). Step 6: For vertex (0,5,0), the space diagonal goes to (8,0,4). Step 7: For vertex (8,5,0), the space diagonal goes to (0,0,4). Step 8: Since each diagonal is counted twice when considering connections from both endpoints, we divide the total by 2: 8 vertices × 1 connection each ÷ 2 = 4 distinct space diagonals. The answer is 4.

3. Emma is conducting a science experiment to track plant growth. She measures the height of her sunflower plant each week. In Week 1, the plant was 12.5 cm tall. By Week 2, it had grown by 15%. In Week 3, it grew by an additional 8% of its Week 2 height. What was the height of Emma's sunflower plant at the end of Week 3? Round your answer to the nearest tenth of a centimeter. Answer: 15.5 Solution: Calculate the height at the end of Week 2. The plant grew by 15% from its Week 1 height of 12.5 cm. 15% of 12.5 cm = 0.15 × 12.5 = 1.875 cm.
   Full step-by-step solution

   Step 1: Calculate the height at the end of Week 2. The plant grew by 15% from its Week 1 height of 12.5 cm. 15% of 12.5 cm = 0.15 × 12.5 = 1.875 cm. New height = 12.5 cm + 1.875 cm = 14.375 cm. Step 2: Calculate the height at the end of Week 3. The plant grew by 8% from its Week 2 height of 14.375 cm. 8% of 14.375 cm = 0.08 × 14.375 = 1.15 cm. New height = 14.375 cm + 1.15 cm = 15.525 cm. Step 3: Round the final answer to the nearest tenth of a centimeter. 15.525 cm rounded to the nearest tenth is 15.5 cm. The final height of the sunflower plant at the end of Week 3 was 15.5 cm.

4. The bar graph below shows the number of books read by five students in a month. Isabella read 12 books, Mason read 9 books, Charlotte read 15 books, Liam read 8 books, and Ava read 11 books. What is the mean number of books read by these five students? Answer: 11 Solution: Add the number of books read by all five students: 12 + 9 + 15 + 8 + 11 = 55. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 55 ÷ 5 = 11.
   Full step-by-step solution

   Step 1: Add the number of books read by all five students: 12 + 9 + 15 + 8 + 11 = 55. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 55 ÷ 5 = 11. The mean number of books read is 11.

5. Liam is tracking his reading progress for a school challenge. He read for 45 minutes on Monday, 60 minutes on Tuesday, 30 minutes on Wednesday, 75 minutes on Thursday, and 50 minutes on Friday. What was the mean number of minutes Liam spent reading each day? Answer: 52 Solution: To find the mean number of minutes Liam spent reading each day, we need to calculate the average. The mean is found by adding up all the daily reading times and then dividing by the number of days. Monday: 45 Tuesday: 60 Wednesday: 30 Thursday: 75 Friday: 50 Sum = 45 + 60 + 30 + 75 + 50 First,…
   Full step-by-step solution

   To find the mean number of minutes Liam spent reading each day, we need to calculate the average. The mean is found by adding up all the daily reading times and then dividing by the number of days. Step 1: Add up all the minutes he read. Monday: 45 Tuesday: 60 Wednesday: 30 Thursday: 75 Friday: 50 Sum = 45 + 60 + 30 + 75 + 50 First, 45 + 60 = 105 105 + 30 = 135 135 + 75 = 210 210 + 50 = 260 So, total minutes = 260. Step 2: Count the number of days. He read for 5 days (Monday through Friday). Step 3: Divide the total minutes by the number of days to get the mean. Mean = 260 / 5 260 ÷ 5 = 52. Thus, the mean number of minutes Liam spent reading each day is 52.

6. Ava surveyed 1,261 students in her city about their favorite type of sport to watch. She displayed the results in a bar graph. The bar for Basketball showed 441 students, the bar for Soccer showed 336 students, the bar for Tennis showed 126 students, and the bar for Baseball showed the remaining students. What is the mode of the data set representing the number of students who chose each sport? Answer: No mode Solution: Find the number of students who chose Baseball. Total students = 1,261 Basketball = 441 Soccer = 336 Tennis = 126 Baseball = 1,261 - (441 + 336 + 126) = 1,261 - 903 = 358 students List the four numbers: 441, 336, 126, 358.
   Full step-by-step solution

   Step 1: Find the number of students who chose Baseball. Total students = 1,261 Basketball = 441 Soccer = 336 Tennis = 126 Baseball = 1,261 - (441 + 336 + 126) = 1,261 - 903 = 358 students Step 2: List the four numbers: 441, 336, 126, 358. Step 3: Check for the mode. Each number appears exactly once. No value repeats. Therefore, there is no mode. The answer is no mode.

7. The dot plot below shows the number of books read by each student in Isabella's class over the summer. Each dot represents one student. Number of books: 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 18, 20 What is the median number of books read? Answer: 12 Solution: List the data in order: 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 18, 20 Count the number of data points. There are 19 numbers. Since 19 is odd, the median is the middle number.
   Full step-by-step solution

   Step 1: List the data in order: 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 17, 18, 20 Step 2: Count the number of data points. There are 19 numbers. Step 3: Since 19 is odd, the median is the middle number. The middle position is (19+1)/2 = 10th position. Step 4: Count to the 10th number: 8(1), 9(2), 9(3), 10(4), 10(5), 10(6), 11(7), 11(8), 12(9), 12(10). The 10th number is 12. The median number of books read is 12.