Data Interpretation

lessonbunny.com

Answer Key & Explanations

Data Interpretation · Grade 6 · Worksheet 1

1. The stem-and-leaf plot below shows the number of books read by 12 students in a Grade 6 class over the summer. Stem | Leaf 3 | 2 5 8 4 | 0 1 4 7 9 5 | 1 3 6 6 | 0 2 Key: 3|2 means 32 books What is the range of the number of books read? Answer: 30 Solution: Identify the smallest value from the stem-and-leaf plot. The smallest stem is 3 with leaf 2, so 32 books. Step 2: Identify the largest value.
   Full step-by-step solution

   Step 1: Identify the smallest value from the stem-and-leaf plot. The smallest stem is 3 with leaf 2, so 32 books. Step 2: Identify the largest value. The largest stem is 6 with leaf 2, so 62 books. Step 3: Calculate the range: 62 - 32 = 30. The answer is 30.

2. 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.

3. Noah surveyed 1,200 students in his school about their favorite type of pizza topping. He recorded the results in the table below. How many more students prefer pepperoni than prefer mushrooms? Answer: 120 students Solution: Find the number of students who prefer pepperoni. Pepperoni is 35% of 1,200 students. 35% of 1,200 = 0.35 x 1,200 = 420 students.
   Full step-by-step solution

   Step 1: Find the number of students who prefer pepperoni. Pepperoni is 35% of 1,200 students. 35% of 1,200 = 0.35 x 1,200 = 420 students. Step 2: Find the number of students who prefer mushrooms. Mushrooms are 25% of 1,200 students. 25% of 1,200 = 0.25 x 1,200 = 300 students. Step 3: Subtract to find how many more prefer pepperoni than mushrooms. 420 - 300 = 120 students. The answer is 120 students.

4. A school cafeteria tracked the number of pizza slices sold each day for a week. The data shows: Monday - 125 slices, Tuesday - 138 slices, Wednesday - 142 slices, Thursday - 157 slices, Friday - 168 slices. What is the mean number of pizza slices sold per day? Answer: 146 Solution: To find the mean number of pizza slices sold per day, we need to calculate the average. The mean is found by adding up all the values and then dividing by the number of days. 125 + 138 = 263 263 + 142 = 405 405 + 157 = 562 562 + 168 = 730 So the total slices sold in the week is 730.
   Full step-by-step solution

   To find the mean number of pizza slices sold per day, we need to calculate the average. The mean is found by adding up all the values and then dividing by the number of days. Step 1: Add up the slices sold for all days. 125 + 138 = 263 263 + 142 = 405 405 + 157 = 562 562 + 168 = 730 So the total slices sold in the week is 730. Step 2: Count the number of days. The data is from Monday to Friday, so there are 5 days. Step 3: Divide the total slices by the number of days. Mean = 730 / 5 Step 4: Perform the division. 730 ÷ 5 = 146 So the mean number of pizza slices sold per day is 146.

5. Liam is planning a school fundraiser and needs to create a budget. He has $3,200 total to allocate. He plans to spend 35% on supplies, 28% on advertising, and 18% on venue rental. The remaining money will be used for prizes. How much money, in dollars, is allocated for prizes? Answer: 608 Solution: Calculate the total percentage spent on supplies, advertising, and venue rental. 35% + 28% + 18% = 81% Calculate the percentage remaining for prizes. 100% - 81% = 19% Calculate 19% of $3,200.
   Full step-by-step solution

   Step 1: Calculate the total percentage spent on supplies, advertising, and venue rental. 35% + 28% + 18% = 81% Step 2: Calculate the percentage remaining for prizes. 100% - 81% = 19% Step 3: Calculate 19% of $3,200. 19% of 3,200 = 0.19 × 3,200 = 608 The answer is $608.

6. The line graph below shows the number of books read by Sophia each month from January to June. January: 12, February: 15, March: 9, April: 18, May: 22, June: 14. What is the median number of books Sophia read per month? Answer: 14.5 Solution: List the numbers of books read each month: 12, 15, 9, 18, 22, 14. Arrange the numbers in order from least to greatest: 9, 12, 14, 15, 18, 22.
   Full step-by-step solution

   Step 1: List the numbers of books read each month: 12, 15, 9, 18, 22, 14. Step 2: Arrange the numbers in order from least to greatest: 9, 12, 14, 15, 18, 22. Step 3: Since there are 6 numbers (an even amount), the median is the average of the two middle numbers. The two middle numbers are the 3rd and 4th numbers: 14 and 15. Step 4: Calculate the average: (14 + 15) ÷ 2 = 29 ÷ 2 = 14.5. The median number of books Sophia read per month is 14.5.

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.

8. 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.