Data Display

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Data Display · Grade 6 · Worksheet 2

1. Mason recorded the ages (in years) of 15 people at a community center: 8, 12, 15, 15, 18, 18, 18, 21, 21, 21, 24, 24, 27, 30, 33. Create a histogram with intervals of 6 years (starting at 8 and ending at 38). How many people are in the interval that contains the most ages? Answer: 5 Solution: Define the intervals of 6 years starting from 8: 8-13, 14-19, 20-25, 26-31, 32-37.
   Full step-by-step solution

   Step 1: Define the intervals of 6 years starting from 8: 8-13, 14-19, 20-25, 26-31, 32-37. Step 2: Count ages in each interval: - 8-13: 8, 12 = 2 people - 14-19: 15, 15, 18, 18, 18 = 5 people - 20-25: 21, 21, 21, 24, 24 = 5 people - 26-31: 27, 30 = 2 people - 32-37: 33 = 1 person Step 3: The intervals 14-19 and 20-25 both have the most people (5 each). Step 4: The answer is 5 people. The answer is 5.

2. A rectangular city park is drawn on a coordinate plane with corners at (0, 0), (1200, 0), (1200, 800), and (0, 800). A circular pond with a diameter of 200 units is placed in the park with its center at (600, 400). What percentage of the park's total area is occupied by the pond? (Use π = 3.14) Answer: 3.27% Solution: Length = 1200 units, Width = 800 units Area of rectangle = length × width = 1200 × 800 = 960,000 square units Diameter = 200 units, so radius = 100 units Area of circle = π × radius² = 3.14 × 100² = 3.14 × 10,000 = 31,400 square units Percentage = (pond area ÷ park area) × 100 Percentage =…
   Full step-by-step solution

   Step 1: Find the area of the rectangular park Length = 1200 units, Width = 800 units Area of rectangle = length × width = 1200 × 800 = 960,000 square units Step 2: Find the area of the circular pond Diameter = 200 units, so radius = 100 units Area of circle = π × radius² = 3.14 × 100² = 3.14 × 10,000 = 31,400 square units Step 3: Calculate what percentage the pond is of the park Percentage = (pond area ÷ park area) × 100 Percentage = (31,400 ÷ 960,000) × 100 Step 4: Perform the division 31,400 ÷ 960,000 = 0.032708333... Step 5: Multiply by 100 to get percentage 0.032708333... × 100 = 3.2708333...% Step 6: Round to two decimal places 3.27% The answer is 3.27%.

3. (3/4 + 1/2) × 120 = ? Answer: 150 Solution: To add these fractions, they must have the same denominator. The least common denominator of 4 and 2 is 4. Convert 1/2 to a fraction with denominator 4: 1/2 = (1 × 2)/(2 × 2) = 2/4.
   Full step-by-step solution

   Let's solve step-by-step. Step 1: First, we need to calculate 3/4 + 1/2. To add these fractions, they must have the same denominator. The least common denominator of 4 and 2 is 4. Step 2: Convert 1/2 to a fraction with denominator 4: 1/2 = (1 × 2)/(2 × 2) = 2/4. Step 3: Now add: 3/4 + 2/4 = (3 + 2)/4 = 5/4. Step 4: The problem says: (3/4 + 1/2) × 120 = (5/4) × 120. Step 5: Multiply 5/4 by 120: (5 × 120) / 4 = 600 / 4. Step 6: Divide 600 by 4: 600 ÷ 4 = 150. Final answer: 150

4. Emma is planning a school bake sale and needs to make cookies for her classmates. She found a recipe that requires 2 1/4 cups of flour for 3 dozen cookies. If Emma wants to make 8 dozen cookies for the bake sale, how many cups of flour will she need? Answer: 6 Solution: Find how much flour is needed for 1 dozen cookies 2 1/4 cups ÷ 3 = 9/4 ÷ 3 = 9/4 × 1/3 = 9/12 = 3/4 cup per dozen Calculate flour needed for 8 dozen cookies 3/4 cup × 8 = 24/4 = 6 cups Emma will need 6 cups of flour for 8 dozen cookies.
   Full step-by-step solution

   Step 1: Find how much flour is needed for 1 dozen cookies 2 1/4 cups ÷ 3 = 9/4 ÷ 3 = 9/4 × 1/3 = 9/12 = 3/4 cup per dozen Step 2: Calculate flour needed for 8 dozen cookies 3/4 cup × 8 = 24/4 = 6 cups Emma will need 6 cups of flour for 8 dozen cookies.

5. Liam surveyed his classmates about the number of books they read over summer break. He recorded the following data: 5, 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 30, 30, 35. Create a dot plot of this data. Then, determine the median number of books read. Answer: 20 Solution: List the data in order (already given): 5, 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 30, 30, 35. Count the number of data points. There are 16 values.
   Full step-by-step solution

   Step 1: List the data in order (already given): 5, 10, 10, 15, 15, 15, 20, 20, 20, 20, 25, 25, 25, 30, 30, 35. Step 2: Count the number of data points. There are 16 values. Step 3: Since there is an even number of data points, the median is the average of the 8th and 9th values. Step 4: The 8th value is 20, and the 9th value is 20. Step 5: Average = (20 + 20) / 2 = 40 / 2 = 20. The answer is 20.

6. Create a dot plot for the following data set: 12, 15, 15, 18, 18, 18, 21, 21, 24, 27 Answer: Dot plot with points at 12 (1), 15 (2), 18 (3), 21 (2), 24 (1), 27 (1) Solution: List the unique values in order: 12, 15, 18, 21, 24, 27.
   Full step-by-step solution

   Step 1: List the unique values in order: 12, 15, 18, 21, 24, 27. Step 2: Count how many times each value appears: 12 appears 1 time 15 appears 2 times 18 appears 3 times 21 appears 2 times 24 appears 1 time 27 appears 1 time Step 3: Draw a horizontal number line from 12 to 27 with tick marks at each of these values. Step 4: Above each value, draw one dot for each occurrence: Above 12: 1 dot Above 15: 2 dots Above 18: 3 dots Above 21: 2 dots Above 24: 1 dot Above 27: 1 dot The final dot plot shows the distribution of the data with a cluster around 18.

7. Emma is planning a school bake sale and needs to make a profit of at least $200. She buys ingredients for $85 and plans to sell cupcakes for $2.50 each. She also needs to pay $45 to rent a table. How many cupcakes does Emma need to sell to reach her profit goal? Answer: 132 Solution: Ingredients cost: $85 Table rental: $45 Total costs = $85 + $45 = $130 Profit goal: $200 Total revenue needed = Profit + Total costs Total revenue needed = $200 + $130 = $330 Price per cupcake: $2.50 Number of cupcakes = Total revenue needed ÷ Price per cupcake Number of cupcakes = $330 ÷ $2.50…
   Full step-by-step solution

   Step 1: Calculate Emma's total costs Ingredients cost: $85 Table rental: $45 Total costs = $85 + $45 = $130 Step 2: Determine the total revenue needed Profit goal: $200 Total revenue needed = Profit + Total costs Total revenue needed = $200 + $130 = $330 Step 3: Calculate how many cupcakes she needs to sell Price per cupcake: $2.50 Number of cupcakes = Total revenue needed ÷ Price per cupcake Number of cupcakes = $330 ÷ $2.50 = 132 Emma needs to sell 132 cupcakes to reach her profit goal.

8. Emma is planning a school bake sale and needs to make a large batch of cookies. The recipe requires 2 1/4 cups of flour for every 3 dozen cookies. If Emma wants to make 15 dozen cookies for the sale, and she already has 8 cups of flour at home, how many more cups of flour does she need to buy? Answer: 3.25 Solution: 2 1/4 cups ÷ 3 dozen = 9/4 cups ÷ 3 = 9/4 × 1/3 = 9/12 = 3/4 cup per dozen Calculate total flour needed for 15 dozen cookies 15 dozen × 3/4 cup per dozen = 15 × 3/4 = 45/4 = 11 1/4 cups 11 1/4 cups = 11.25 cups 11.25 cups needed - 8 cups available = 3.25 cups Emma needs to buy 3.25 more cups of…
   Full step-by-step solution

   Step 1: Find how much flour is needed per dozen cookies 2 1/4 cups ÷ 3 dozen = 9/4 cups ÷ 3 = 9/4 × 1/3 = 9/12 = 3/4 cup per dozen Step 2: Calculate total flour needed for 15 dozen cookies 15 dozen × 3/4 cup per dozen = 15 × 3/4 = 45/4 = 11 1/4 cups Step 3: Convert to decimal for easier calculation 11 1/4 cups = 11.25 cups Step 4: Subtract flour Emma already has 11.25 cups needed - 8 cups available = 3.25 cups Emma needs to buy 3.25 more cups of flour.