Data Interpretation

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Data Interpretation · Grade 6 · Worksheet 1

1. Liam is tracking his reading progress for a school challenge. He read 120 pages on Monday, which was 25% more than he read on Sunday. On Tuesday, he read 15% fewer pages than on Monday. How many pages did Liam read in total from Sunday to Tuesday? Answer: 318 Solution: We know Monday = 120 pages, which is 25% more than Sunday. Let Sunday pages = \( S \). 25% more means: Monday = \( S + 0.25S = 1.25S \) \( 1.25S = 120 \) \( S = 120 / 1.25 \) \( S = 96 \) So Sunday: 96 pages.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find pages read on Sunday** We know Monday = 120 pages, which is 25% more than Sunday. Let Sunday pages = \( S \). 25% more means: Monday = \( S + 0.25S = 1.25S \) So: \( 1.25S = 120 \) \( S = 120 / 1.25 \) \( S = 96 \) So Sunday: 96 pages. --- **Step 2: Find pages read on Tuesday** Tuesday: 15% fewer than Monday. 15% of Monday = \( 0.15 \times 120 = 18 \) Fewer means subtract: Tuesday = \( 120 - 18 = 102 \) pages. --- **Step 3: Find total pages from Sunday to Tuesday** Total = Sunday + Monday + Tuesday Total = \( 96 + 120 + 102 \) Total = \( 216 + 102 = 318 \) --- **Final Answer:** 318

2. 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.

3. The bar graph below shows the number of books read by five students in a month. Emma read 25 books, Liam read 30 books, Olivia read 20 books, Noah read 35 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 + 30 + 20 + 35 + 40 = 150. 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 + 30 + 20 + 35 + 40 = 150. 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.

4. 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.

5. A school is organizing a field trip to a science museum. There are 324 students going on the trip, and each school bus can carry 42 students. The bus company charges $185 per bus for the trip. What is the total cost for bus transportation? Answer: $1480 Solution: Calculate how many buses are needed by dividing the number of students by the bus capacity: 324 ÷ 42 = 7.714...
   Full step-by-step solution

   Step 1: Calculate how many buses are needed by dividing the number of students by the bus capacity: 324 ÷ 42 = 7.714... Step 2: Since you can't have a fraction of a bus, round up to the next whole number: 8 buses are needed Step 3: Calculate the total cost by multiplying the number of buses by the cost per bus: 8 × $185 = $1480 Step 4: The total cost for bus transportation is $1480

6. The stem-and-leaf plot below shows the number of books read by 11 students in a Grade 6 class over summer break. Stem | Leaf 3 | 1 5 7 4 | 0 2 3 8 5 | 1 4 9 6 | 0 Key: 3 | 1 means 31 books What is the median number of books read? Answer: 43 Solution: 31, 35, 37, 40, 42, 43, 48, 51, 54, 59, 60 There are 11 data values (odd number). The median is the middle value, which is the 6th value when ordered.
   Full step-by-step solution

   Step 1: List all data values from the stem-and-leaf plot: 31, 35, 37, 40, 42, 43, 48, 51, 54, 59, 60 Step 2: There are 11 data values (odd number). The median is the middle value, which is the 6th value when ordered. Step 3: Count to the 6th value: 31 (1st), 35 (2nd), 37 (3rd), 40 (4th), 42 (5th), 43 (6th). Step 4: The median is 43. The answer is 43.

7. The bar graph shows the number of books read by five students in a month: Emma read 15, Liam read 25, Olivia read 20, Noah read 10, and Ava read 30. What is the mean number of books read? Answer: 20 Solution: Add all the books read: 15 + 25 + 20 + 10 + 30 = 100. Count the number of students: 5. Divide the total by the number of students: 100 ÷ 5 = 20.
   Full step-by-step solution

   Step 1: Add all the books read: 15 + 25 + 20 + 10 + 30 = 100. Step 2: Count the number of students: 5. Step 3: Divide the total by the number of students: 100 ÷ 5 = 20. The mean number of books read is 20.

8. 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: 21, June: 14. What is the mean number of books read per month? Answer: 14.83 Solution: Add the number of books for all six months: 12 + 15 + 9 + 18 + 21 + 14 = 89. Divide the total by the number of months: 89 ÷ 6 = 14.8333... Round to two decimal places: 14.83.
   Full step-by-step solution

   Step 1: Add the number of books for all six months: 12 + 15 + 9 + 18 + 21 + 14 = 89. Step 2: Divide the total by the number of months: 89 ÷ 6 = 14.8333... Step 3: Round to two decimal places: 14.83. The mean number of books read per month is 14.83.