Data Display

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Answer Key & Explanations

Data Display · Grade 6 · Worksheet 1

1. A rectangular city park is drawn on a coordinate plane with corners at (0, 0), (120, 0), (120, 80), and (0, 80). A circular pond with a diameter of 40 units is placed in the park with its center at (60, 40). What percentage of the park's total area is occupied by the pond? (Use π = 3.14) Answer: 13.08% Solution: Length = 120 units, Width = 80 units Area of rectangle = length × width = 120 × 80 = 9,600 square units Diameter = 40 units, so radius = 20 units Area of circle = π × radius² = 3.14 × 20² = 3.14 × 400 = 1,256 square units Percentage = (pond area ÷ park area) × 100 Percentage = (1,256 ÷ 9,600) ×…
   Full step-by-step solution

   Step 1: Find the area of the rectangular park Length = 120 units, Width = 80 units Area of rectangle = length × width = 120 × 80 = 9,600 square units Step 2: Find the area of the circular pond Diameter = 40 units, so radius = 20 units Area of circle = π × radius² = 3.14 × 20² = 3.14 × 400 = 1,256 square units Step 3: Find what percentage the pond is of the park Percentage = (pond area ÷ park area) × 100 Percentage = (1,256 ÷ 9,600) × 100 Step 4: Calculate the division 1,256 ÷ 9,600 = 0.130833... Step 5: Multiply by 100 to get percentage 0.130833... × 100 = 13.0833...% Step 6: Round to two decimal places 13.08% The answer is 13.08%.

2. Isabella recorded the number of books each student in her class read over the summer. The data set is: 8, 12, 12, 15, 15, 15, 18, 18, 18, 18, 21, 21, 21, 24, 24, 27. Create a dot plot of this data on a number line from 8 to 27. How many students read more than 18 books? Answer: 6 Solution: List the data in order: 8, 12, 12, 15, 15, 15, 18, 18, 18, 18, 21, 21, 21, 24, 24, 27.
   Full step-by-step solution

   Step 1: List the data in order: 8, 12, 12, 15, 15, 15, 18, 18, 18, 18, 21, 21, 21, 24, 24, 27. Step 2: Count how many students read each number of books: 8: 1 student 12: 2 students 15: 3 students 18: 4 students 21: 3 students 24: 2 students 27: 1 student Step 3: Identify numbers greater than 18: 21, 24, 27. Step 4: Add the counts for these numbers: 3 (for 21) + 2 (for 24) + 1 (for 27) = 6 students. The answer is 6.

3. Create a box plot for the data: 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307 Answer: Minimum = 1022, Q1 = 1082, Median = 1157, Q3 = 1232, Maximum = 1307 Solution: Order the data (already in order): 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307 There are 20 numbers.
   Full step-by-step solution

   Step 1: Order the data (already in order): 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307 Step 2: There are 20 numbers. The median is the average of the 10th and 11th values: (1157 + 1172) / 2 = 2329 / 2 = 1164.5 Step 3: Lower half (first 10 numbers): 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157. Q1 is the median of this half: average of 5th and 6th values = (1082 + 1097) / 2 = 2179 / 2 = 1089.5 Step 4: Upper half (last 10 numbers): 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307. Q3 is the median of this half: average of 5th and 6th values = (1232 + 1247) / 2 = 2479 / 2 = 1239.5 Step 5: Minimum = 1022, Maximum = 1307 Step 6: Box plot summary: Min = 1022, Q1 = 1089.5, Median = 1164.5, Q3 = 1239.5, Max = 1307

4. Olivia is a meteorologist tracking daily high temperatures (°F) for a city over two weeks. She recorded these temperatures: 65, 70, 70, 75, 75, 75, 80, 80, 80, 80, 85, 85, 90, 95. She wants to display the data in a box plot. What is the value of the third quartile (Q3) in this data set? Answer: 85 Solution: Arrange the data in order: 65, 70, 70, 75, 75, 75, 80, 80, 80, 80, 85, 85, 90, 95 Find the median (Q2). There are 14 numbers, so the median is the average of the 7th and 8th numbers: (80 + 80) / 2 = 80.
   Full step-by-step solution

   Step 1: Arrange the data in order: 65, 70, 70, 75, 75, 75, 80, 80, 80, 80, 85, 85, 90, 95 Step 2: Find the median (Q2). There are 14 numbers, so the median is the average of the 7th and 8th numbers: (80 + 80) / 2 = 80. Step 3: The upper half of the data (numbers greater than the median) is: 80, 80, 85, 85, 90, 95. There are 6 numbers. Step 4: The median of the upper half (Q3) is the average of the 3rd and 4th numbers in the upper half: (85 + 85) / 2 = 85. The third quartile is 85.

5. Create a dot plot for the data: 8, 9, 9, 10, 10, 10, 12, 12, 14, 15 Answer: Dot plot with points at 8 (1), 9 (2), 10 (3), 12 (2), 14 (1), 15 (1) Solution: List the data values in order: 8, 9, 9, 10, 10, 10, 12, 12, 14, 15. For each value, place a dot above that number on the line.
   Full step-by-step solution

   Step 1: List the data values in order: 8, 9, 9, 10, 10, 10, 12, 12, 14, 15. Step 2: Draw a horizontal number line from 8 to 15. Step 3: For each value, place a dot above that number on the line. Count the frequency: 8 appears once (1 dot), 9 appears twice (2 dots), 10 appears three times (3 dots), 12 appears twice (2 dots), 14 appears once (1 dot), 15 appears once (1 dot). Step 4: The final dot plot shows the distribution of the data with the correct number of dots above each value.

6. Create a box plot for the data: 8, 12, 15, 19, 22, 22, 25, 28, 31, 35, 42 Answer: Min=8, Q1=15, Median=22, Q3=31, Max=42 Solution: Order the data: 8, 12, 15, 19, 22, 22, 25, 28, 31, 35, 42 Minimum = 8, Maximum = 42 Median (middle value): There are 11 numbers, so the 6th value is the median: 22 Lower half (numbers below median): 8, 12, 15, 19, 22.
   Full step-by-step solution

   Step 1: Order the data: 8, 12, 15, 19, 22, 22, 25, 28, 31, 35, 42 Step 2: Minimum = 8, Maximum = 42 Step 3: Median (middle value): There are 11 numbers, so the 6th value is the median: 22 Step 4: Lower half (numbers below median): 8, 12, 15, 19, 22. Median of lower half (Q1) = 15 Step 5: Upper half (numbers above median): 25, 28, 31, 35, 42. Median of upper half (Q3) = 31 Step 6: Box plot summary: Min=8, Q1=15, Median=22, Q3=31, Max=42

7. Mere surveyed 24 students in her class to find out how many books they read over the summer. The number of books read by each student is listed below: 2, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 18, 18, 20, 20, 22, 24, 26. Create a dot plot of this data. How many students read exactly 14 books? Answer: 3 Solution: List all the data points: 2, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 18, 18, 20, 20, 22, 24, 26. Count how many times the number 14 appears in the list.
   Full step-by-step solution

   Step 1: List all the data points: 2, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 18, 18, 20, 20, 22, 24, 26. Step 2: Count how many times the number 14 appears in the list. We see 14 appears three times (positions 13, 14, and 15 in the list). Step 3: Therefore, 3 students read exactly 14 books. The answer is 3.

8. Create a dot plot for the data: 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307 Answer: A dot plot with a horizontal axis from 1022 to 1307, each data point represented by a single dot above its value, all dots in a single row showing the evenly spaced distribution. Solution: Mark tick marks at each of the given values: 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307.
   Full step-by-step solution

   Step 1: Draw a horizontal number line from 1022 to 1307. Mark tick marks at each of the given values: 1022, 1037, 1052, 1067, 1082, 1097, 1112, 1127, 1142, 1157, 1172, 1187, 1202, 1217, 1232, 1247, 1262, 1277, 1292, 1307. Step 2: For each data point, place one dot directly above its value on the number line. Since there are 20 data points and each value appears exactly once, place exactly one dot above each tick mark. Step 3: The resulting dot plot will have a single row of 20 dots, each spaced 15 units apart, forming a straight horizontal line from 1022 to 1307. The final answer is a dot plot with one dot at each of the 20 values listed.