Data Display

lessonbunny.com

Answer Key & Explanations

Data Display · Grade 6 · Worksheet 3

1. Noah is planning a school fundraiser selling custom t-shirts. He needs to order shirts in three sizes: small, medium, and large. The ratio of small to medium to large shirts should be 2:3:4. If Noah wants to order a total of 270 shirts, how many large shirts should he order? Answer: 120 Solution: The ratio of small:medium:large shirts is 2:3:4 Add all parts of the ratio: 2 + 3 + 4 = 9 parts total Divide the total shirts by the total parts: 270 ÷ 9 = 30 shirts per part Multiply the number of parts for large shirts by the shirts per part: 4 × 30 = 120 Noah should order 120 large shirts.
   Full step-by-step solution

   Step 1: The ratio of small:medium:large shirts is 2:3:4 Step 2: Add all parts of the ratio: 2 + 3 + 4 = 9 parts total Step 3: Divide the total shirts by the total parts: 270 ÷ 9 = 30 shirts per part Step 4: Multiply the number of parts for large shirts by the shirts per part: 4 × 30 = 120 Noah should order 120 large shirts.

2. Create a box plot for the data: 11, 15, 18, 22, 22, 25, 28, 30, 33, 37, 42 Answer: Minimum: 11, Q1: 18, Median: 25, Q3: 33, Maximum: 42 Solution: Order the data: 11, 15, 18, 22, 22, 25, 28, 30, 33, 37, 42 (already in order). Find the median (middle value). There are 11 numbers, so the median is the 6th number: 25.
   Full step-by-step solution

   Step 1: Order the data: 11, 15, 18, 22, 22, 25, 28, 30, 33, 37, 42 (already in order). Step 2: Find the median (middle value). There are 11 numbers, so the median is the 6th number: 25. Step 3: Find the lower quartile (Q1), the median of the lower half (numbers below the median). Lower half: 11, 15, 18, 22, 22. There are 5 numbers, so Q1 is the 3rd number: 18. Step 4: Find the upper quartile (Q3), the median of the upper half (numbers above the median). Upper half: 28, 30, 33, 37, 42. There are 5 numbers, so Q3 is the 3rd number: 33. Step 5: Identify the minimum: 11 and maximum: 42. Step 6: The five-number summary is: Minimum = 11, Q1 = 18, Median = 25, Q3 = 33, Maximum = 42. Draw a box from Q1 to Q3 with a line at the median, and whiskers from the minimum to Q1 and from Q3 to the maximum.

3. Emma recorded the number of pages she read each day for 15 days: 23, 25, 25, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 33, 35. Create a box plot of this data. What is the interquartile range (IQR) of the number of pages she read? Answer: 4 Solution: Order the data (already in order): 23, 25, 25, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 33, 35 Find the median (Q2). There are 15 data points, so the median is the 8th value: 29.
   Full step-by-step solution

   Step 1: Order the data (already in order): 23, 25, 25, 27, 27, 27, 29, 29, 29, 29, 31, 31, 31, 33, 35 Step 2: Find the median (Q2). There are 15 data points, so the median is the 8th value: 29. Step 3: Lower half (first 7 values): 23, 25, 25, 27, 27, 27, 29. The median of the lower half is the 4th value: 27. So Q1 = 27. Step 4: Upper half (last 7 values): 29, 29, 31, 31, 31, 33, 35. The median of the upper half is the 4th value: 31. So Q3 = 31. Step 5: Interquartile range (IQR) = Q3 - Q1 = 31 - 27 = 4. The answer is 4.

4. Create a dot plot for the data: 13, 15, 15, 17, 17, 17, 19, 19, 21, 23 Answer: A dot plot with a number line from 13 to 23, with dots above each number: one dot above 13, two dots above 15, three dots above 17, two dots above 19, one dot above 21, one dot above 23. Solution: For each data value, place a dot above the corresponding number. - 13 appears once: one dot above 13. - 15 appears twice: two dots above 15.
   Full step-by-step solution

   Step 1: Draw a horizontal number line from 13 to 23, marking each integer: 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. Step 2: For each data value, place a dot above the corresponding number. - 13 appears once: one dot above 13. - 15 appears twice: two dots above 15. - 17 appears three times: three dots above 17. - 19 appears twice: two dots above 19. - 21 appears once: one dot above 21. - 23 appears once: one dot above 23. Step 3: The dot plot shows the frequency of each value. The final dot plot has dots stacked vertically at each number as described.

5. Noah is planning a school fundraiser selling custom T-shirts. He found a supplier that charges $8.50 per shirt for orders up to 100 shirts, but offers a 15% discount for orders over 100 shirts. If Noah wants to order 120 shirts for the fundraiser, and the school charges him an additional $85 for printing equipment, what will be Noah's total cost? Answer: $952 Solution: 120 shirts × $8.50 per shirt = $1,020 Calculate the 15% discount amount 15% of $1,020 = 0.15 × $1,020 = $153 $1,020 - $153 = $867 $867 + $85 = $952 The answer is $952.
   Full step-by-step solution

   Step 1: Calculate the original cost without discount 120 shirts × $8.50 per shirt = $1,020 Step 2: Calculate the 15% discount amount 15% of $1,020 = 0.15 × $1,020 = $153 Step 3: Calculate the discounted shirt cost $1,020 - $153 = $867 Step 4: Add the printing equipment fee $867 + $85 = $952 The answer is $952.

6. Create a dot plot for the data: 9, 10, 10, 11, 12, 12, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25 Answer: A dot plot with numbers 9 to 25 on the horizontal axis, each data point represented by a dot above its value: 9:1, 10:2, 11:1, 12:3, 13:1, 14:1, 15:2, 16:1, 17:1, 18:1, 19:1, 20:1, 21:1, 22:1, 23:1, 25:1 Solution: Identify the smallest value (9) and the largest value (25) to set the scale from 9 to 25. For each data point, place a dot above its corresponding number. If a number appears more than once, stack the dots vertically.
   Full step-by-step solution

   Step 1: Identify the smallest value (9) and the largest value (25) to set the scale from 9 to 25. Step 2: Draw a horizontal number line labeled from 9 to 25, marking each integer. Step 3: For each data point, place a dot above its corresponding number. If a number appears more than once, stack the dots vertically. Step 4: Count the frequency for each number: 9: 1 dot 10: 2 dots 11: 1 dot 12: 3 dots 13: 1 dot 14: 1 dot 15: 2 dots 16: 1 dot 17: 1 dot 18: 1 dot 19: 1 dot 20: 1 dot 21: 1 dot 22: 1 dot 23: 1 dot 25: 1 dot Step 5: The completed dot plot shows the distribution of the data with stacks of dots representing frequencies. The answer is a dot plot with the above frequencies.

7. Create a histogram for the following data: 8, 12, 15, 19, 22, 22, 25, 28, 31, 35, 42 Answer: Histogram with intervals 8-15, 15-22, 22-29, 29-36, 36-43 and frequencies 3, 2, 3, 2, 1 Solution: Find the range: 42 - 8 = 34. Choose intervals of width 7: 8-15, 15-22, 22-29, 29-36, 36-43.
   Full step-by-step solution

   Step 1: Find the range: 42 - 8 = 34. Choose intervals of width 7: 8-15, 15-22, 22-29, 29-36, 36-43. Step 2: Count frequencies: - 8-15: 8, 12, 15 → 3 - 15-22: 19, 22, 22 → 3 (but 15 is in previous, so 19, 22, 22 → 3) - 22-29: 25, 28 → 2 - 29-36: 31, 35 → 2 - 36-43: 42 → 1 Step 3: Draw the histogram with these intervals on the x-axis and frequencies on the y-axis. The final histogram has bars of heights 3, 3, 2, 2, 1.

8. Matiu surveyed his classmates to find out how many hours they spent on homework last week. Here are the numbers of hours: 2, 4, 4, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 14. Create a dot plot for this data. Then, using your dot plot, determine the median number of hours spent on homework. Answer: 8 Solution: List the data in order: 2, 4, 4, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 14. There are 16 data points (an even number). Step 2: The two middle positions are the 8th and 9th values.
   Full step-by-step solution

   Step 1: List the data in order: 2, 4, 4, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 14. There are 16 data points (an even number). Step 2: The two middle positions are the 8th and 9th values. Counting from the smallest: 1st:2, 2nd:4, 3rd:4, 4th:6, 5th:6, 6th:6, 7th:8, 8th:8, 9th:8, 10th:8, 11th:10, 12th:10, 13th:10, 14th:12, 15th:12, 16th:14. The 8th value is 8 and the 9th value is 8. Step 3: The median is the average of these two numbers: (8 + 8) / 2 = 8. The answer is 8.