Data Interpretation

lessonbunny.com

Answer Key & Explanations

Data Interpretation · Grade 6 · Worksheet 3

1. The bar graph below shows the number of books read by five students in a month. Emma read 9 books, Liam read 13 books, Olivia read 7 books, Noah read 11 books, and Sophia read 15 books. What is the median number of books read? Answer: 11 Solution: List the number of books read: 9, 13, 7, 11, 15. Arrange the numbers in order from least to greatest: 7, 9, 11, 13, 15. Since there are 5 numbers (an odd amount), the median is the middle number.
   Full step-by-step solution

   Step 1: List the number of books read: 9, 13, 7, 11, 15. Step 2: Arrange the numbers in order from least to greatest: 7, 9, 11, 13, 15. Step 3: Since there are 5 numbers (an odd amount), the median is the middle number. Step 4: The middle number is the third number in the list: 11. The answer is 11.

2. Hana surveyed 2,400 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 720 students, the bar for Soccer showed 600 students, the bar for Tennis showed 480 students, and the bar for Swimming showed 360 students. The remaining students chose Other sports. What is the mean number of students who chose each sport category (Basketball, Soccer, Tennis, Swimming, and Other)? Answer: 480 Solution: Find the number of students who chose Other. Total students surveyed = 2,400 Students who chose Basketball = 720 Students who chose Soccer = 600 Students who chose Tennis = 480 Students who chose Swimming = 360 Sum of known categories = 720 + 600 + 480 + 360 = 2,160 Students who chose Other =…
   Full step-by-step solution

   Step 1: Find the number of students who chose Other. Total students surveyed = 2,400 Students who chose Basketball = 720 Students who chose Soccer = 600 Students who chose Tennis = 480 Students who chose Swimming = 360 Sum of known categories = 720 + 600 + 480 + 360 = 2,160 Students who chose Other = 2,400 - 2,160 = 240 Step 2: Add all the numbers for all five categories. 720 + 600 + 480 + 360 + 240 = 2,400 Step 3: Divide the total by the number of categories (5). 2,400 ÷ 5 = 480 The mean number of students who chose each sport category is 480.

3. The bar graph below shows the number of books read by five students in a month. Isabella read 12 books, Mason read 17 books, Charlotte read 22 books, Ethan read 7 books, and Olivia read 27 books. What is the mean number of books read? Answer: 17 Solution: Add the number of books read by all students: 12 + 17 + 22 + 7 + 27 = 85. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 85 ÷ 5 = 17.
   Full step-by-step solution

   Step 1: Add the number of books read by all students: 12 + 17 + 22 + 7 + 27 = 85. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 85 ÷ 5 = 17. The mean number of books read is 17.

4. (-15) × (-4) + 36 ÷ (-9) - 7² = ? Answer: 7 Solution: Evaluate the exponent: 7² = 49. The expression becomes: (-15) × (-4) + 36 ÷ (-9) - 49. Perform multiplication and division from left to right.
   Full step-by-step solution

   Step 1: Evaluate the exponent: 7² = 49. The expression becomes: (-15) × (-4) + 36 ÷ (-9) - 49. Step 2: Perform multiplication and division from left to right. First, (-15) × (-4) = 60. Next, 36 ÷ (-9) = -4. The expression is now: 60 + (-4) - 49. Step 3: Perform addition and subtraction from left to right. First, 60 + (-4) = 56. Then, 56 - 49 = 7. The final answer is 7.

5. The bar graph below shows the number of kilometers that Hana walked each day for one week (Monday to Sunday). Kilometers Walked by Hana Day | Kilometers Monday | 12 Tuesday | 18 Wednesday | 14 Thursday | 22 Friday | 10 Saturday | 26 Sunday | 20 What is the median number of kilometers Hana walked per day? Answer: 18 Solution: List the kilometers walked each day: 12, 18, 14, 22, 10, 26, 20. Arrange the numbers in order from least to greatest: 10, 12, 14, 18, 20, 22, 26.
   Full step-by-step solution

   Step 1: List the kilometers walked each day: 12, 18, 14, 22, 10, 26, 20. Step 2: Arrange the numbers in order from least to greatest: 10, 12, 14, 18, 20, 22, 26. Step 3: Since there are 7 numbers (an odd number), the median is the middle number. The middle number is the 4th number in the ordered list. Step 4: The 4th number is 18. The median number of kilometers Hana walked per day is 18.

6. Sophia surveyed 1,001 students in her town about their favorite type of ice cream flavor. She displayed the results in a bar graph. The bar for Chocolate showed 286 students, the bar for Vanilla showed 221 students, the bar for Strawberry showed 156 students, and the bar for Mint Chip showed 91 students. The remaining students chose Cookie Dough. What is the mode of the data set representing the number of students who chose each flavor? Answer: No mode (or there is no mode) Solution: List the number of students for each flavor. Chocolate: 286 Vanilla: 221 Strawberry: 156 Mint Chip: 91 Cookie Dough: We need to find this. Find the number of students who chose Cookie Dough.
   Full step-by-step solution

   Step 1: List the number of students for each flavor. Chocolate: 286 Vanilla: 221 Strawberry: 156 Mint Chip: 91 Cookie Dough: We need to find this. Step 2: Find the number of students who chose Cookie Dough. Total students = 1,001 Sum of the four known flavors = 286 + 221 + 156 + 91 = 754 Cookie Dough = 1,001 - 754 = 247 Step 3: Now list all five numbers: 286, 221, 156, 91, 247. Check if any number appears more than once. All five numbers are different. Step 4: Since no value repeats, there is no mode. The answer is No mode (or there is no mode).

7. A rectangular garden is drawn on a coordinate plane with corners at (2, 3), (14, 3), (14, 9), and (2, 9). A circular pond with diameter 4 units is placed in the center of the garden. What percentage of the garden's area is occupied by the pond? (Use π = 3.14) Answer: 17.44 Solution: From the coordinates (2,3) to (14,3): length = 14 - 2 = 12 units From the coordinates (2,3) to (2,9): width = 9 - 3 = 6 units Area of rectangle = length × width = 12 × 6 = 72 square units Diameter = 4 units, so radius = 4 ÷ 2 = 2 units Area of circle = π × radius² = 3.14 × 2² = 3.14 × 4 = 12.56…
   Full step-by-step solution

   Step 1: Find the dimensions of the rectangular garden From the coordinates (2,3) to (14,3): length = 14 - 2 = 12 units From the coordinates (2,3) to (2,9): width = 9 - 3 = 6 units Step 2: Calculate the area of the garden Area of rectangle = length × width = 12 × 6 = 72 square units Step 3: Find the radius of the circular pond Diameter = 4 units, so radius = 4 ÷ 2 = 2 units Step 4: Calculate the area of the pond Area of circle = π × radius² = 3.14 × 2² = 3.14 × 4 = 12.56 square units Step 5: Calculate the percentage Percentage = (area of pond ÷ area of garden) × 100 Percentage = (12.56 ÷ 72) × 100 Percentage = 0.174444... × 100 = 17.44% The answer is 17.44.