Data Interpretation

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Data Interpretation · Grade 6 · Worksheet 3

1. The stem-and-leaf plot below shows the number of books read by students in a Grade 6 class over one month. What is the range of the data? Stem | Leaf 2 | 0 2 5 8 3 | 1 4 6 9 4 | 2 5 7 5 | 0 3 Key: 2|0 means 20 books Answer: 33 Solution: Identify the smallest value. The smallest stem is 2 and the smallest leaf on that stem is 0, so the smallest value is 20 books. Identify the largest value.
   Full step-by-step solution

   Step 1: Identify the smallest value. The smallest stem is 2 and the smallest leaf on that stem is 0, so the smallest value is 20 books. Step 2: Identify the largest value. The largest stem is 5 and the largest leaf on that stem is 3, so the largest value is 53 books. Step 3: Calculate the range: 53 - 20 = 33. The answer is 33.

2. The line graph below shows the number of books borrowed from the school library each day for two weeks (Monday to Friday). Week 1: Monday: 48, Tuesday: 52, Wednesday: 64, Thursday: 60, Friday: 56. Week 2: Monday: 44, Tuesday: 56, Wednesday: 68, Thursday: 62, Friday: 50. What is the mean number of books borrowed per day across the two weeks? Answer: 56 Solution: List all book counts from Week 1: 48, 52, 64, 60, 56. Step 2: List all book counts from Week 2: 44, 56, 68, 62, 50. Step 3: Find the total for Week 1: 48 + 52 = 100, 100 + 64 = 164, 164 + 60 = 224, 224 + 56 = 280.
   Full step-by-step solution

   Step 1: List all book counts from Week 1: 48, 52, 64, 60, 56. Step 2: List all book counts from Week 2: 44, 56, 68, 62, 50. Step 3: Find the total for Week 1: 48 + 52 = 100, 100 + 64 = 164, 164 + 60 = 224, 224 + 56 = 280. Step 4: Find the total for Week 2: 44 + 56 = 100, 100 + 68 = 168, 168 + 62 = 230, 230 + 50 = 280. Step 5: Add both totals: 280 + 280 = 560. Step 6: Count the total number of days: 5 days in Week 1 + 5 days in Week 2 = 10 days. Step 7: Divide the total books by the number of days: 560 ÷ 10 = 56. The answer is 56.

3. The bar graph below shows the number of books read by five students in Grade 6 over one month. Number of Books Read: Isabella: 12 books Mason: 7 books Charlotte: 17 books Liam: 22 books Sophia: 12 books What is the mean number of books read by these five students? Round your answer to the nearest whole number. Answer: 14 Solution: Add the number of books read by all students: 12 + 7 + 17 + 22 + 12 = 70 books. There are 5 students. Divide the total by 5: 70 ÷ 5 = 14.
   Full step-by-step solution

   Step 1: Add the number of books read by all students: 12 + 7 + 17 + 22 + 12 = 70 books. Step 2: There are 5 students. Divide the total by 5: 70 ÷ 5 = 14. Step 3: The mean is 14, which is already a whole number. The answer is 14.

4. Liam is conducting a survey about favorite school subjects among 240 students. He creates a pie chart showing that 25% prefer Math, 30% prefer Science, 20% prefer English, and the remaining students prefer Art. How many students prefer Art? Answer: 60 Solution: - 25% prefer Math - 30% prefer Science - 20% prefer English Find the total percentage for Math, Science, and English. 25% + 30% + 20% = 75% Find the percentage that prefer Art.
   Full step-by-step solution

   First, we know the total number of students is 240. The pie chart shows: - 25% prefer Math - 30% prefer Science - 20% prefer English - The rest prefer Art Step 1: Find the total percentage for Math, Science, and English. 25% + 30% + 20% = 75% Step 2: Find the percentage that prefer Art. Since the whole pie chart is 100%, the Art percentage is: 100% - 75% = 25% Step 3: Calculate the number of students who prefer Art. 25% of 240 students means: 25% = 25/100 = 1/4 So, number of Art students = (1/4) * 240 = 240 / 4 = 60 Therefore, 60 students prefer Art.

5. The line plot below shows the number of pages read by each of 13 students in Liam's class during a reading challenge. Each dot represents one student. Number of Pages Read: X X X X X X X X X X X X X X X X X X X X --------------------- 21 23 25 27 29 31 What is the mean number of pages read? (Round your answer to the nearest whole number.) Answer: 27 Solution: - 21 pages: 1 student - 23 pages: 2 students - 25 pages: 3 students - 27 pages: 4 students - 29 pages: 2 students - 31 pages: 1 student 21 x 1 = 21 23 x 2 = 46 25 x 3 = 75 27 x 4 = 108 29 x 2 = 58 31 x 1 = 31 Total = 21 + 46 + 75 + 108 + 58 + 31 = 339 Count the total number of students: 1 + 2 +…
   Full step-by-step solution

   Step 1: Count the number of students for each page value: - 21 pages: 1 student - 23 pages: 2 students - 25 pages: 3 students - 27 pages: 4 students - 29 pages: 2 students - 31 pages: 1 student Step 2: Calculate the total number of pages read: 21 x 1 = 21 23 x 2 = 46 25 x 3 = 75 27 x 4 = 108 29 x 2 = 58 31 x 1 = 31 Total = 21 + 46 + 75 + 108 + 58 + 31 = 339 Step 3: Count the total number of students: 1 + 2 + 3 + 4 + 2 + 1 = 13 Step 4: Calculate the mean: 339 divided by 13 = 26.0769... Step 5: Round to the nearest whole number: 26.0769 rounds to 26. The mean number of pages read is 26.

6. The bar graph below shows the number of books read by five students in a month. Emma read 25 books, Liam read 35 books, Olivia read 20 books, Noah read 30 books, and Ava read 40 books. What is the mean number of books read by these five students? Answer: 30 Solution: Add the number of books read by all students: 25 + 35 + 20 + 30 + 40 = 150 books. Count the number of students: 5. Divide the total by the number of students: 150 ÷ 5 = 30.
   Full step-by-step solution

   Step 1: Add the number of books read by all students: 25 + 35 + 20 + 30 + 40 = 150 books. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 150 ÷ 5 = 30. The mean number of books read is 30.

7. The dot plot below shows the number of books read by 15 students in Kaia's class during a reading challenge. Each dot represents one student. Number of books: 3 5 7 7 9 9 9 11 11 11 11 13 13 15 17 What is the median number of books read? Answer: 11 Solution: Arrange the data in order: 3, 5, 7, 7, 9, 9, 9, 11, 11, 11, 11, 13, 13, 15, 17. There are 15 data points. The median is the middle value, which is the (15 + 1) / 2 = 8th value.
   Full step-by-step solution

   Step 1: Arrange the data in order: 3, 5, 7, 7, 9, 9, 9, 11, 11, 11, 11, 13, 13, 15, 17. Step 2: There are 15 data points. The median is the middle value, which is the (15 + 1) / 2 = 8th value. Step 3: Count to the 8th value: 1st=3, 2nd=5, 3rd=7, 4th=7, 5th=9, 6th=9, 7th=9, 8th=11. The median number of books read is 11.