Math 9 · Unit 15: Interpreting and discussing results · Cambridge Lower Secondary Maths Stage 9

Questions

1. 1. This table shows the results of a Spanish test taken by the learners in class 9R. The first six entries from the table are already on this unordered stem-and-leaf diagram, and stem 2 is done. Drag a number into each empty box to complete stems 0 and 1, with the leaves in the order of the table.

   Fill the blanks with these.

   • 9
   • 2
   • 1
   • 0
   • 7
   • 8
   Check

2. 2. This table shows the results of a Spanish test taken by the learners in class 9R. Complete this ordered stem-and-leaf diagram: drag a number into each empty box. The leaves in each row go in order of size, and stem 2 is done.

   Fill the blanks with these.

   • 5
   • 1
   • 7
   • 8
   • 9
   • 3
   • 6
   Check

3. 3. This table shows the results of a Spanish test taken by the learners in class 9T. The unordered diagram is done. Complete the ordered diagram below it by dragging a number into each empty box.

   Fill the blanks with these.

   • 7
   • 6
   • 1
   • 0
   • 8
   • 9
   • 5
   • 2
   Check

4. 4. Combine the two ordered stem-and-leaf diagrams into one back-to-back diagram, with class 9R on the left and class 9T on the right. Drag a number into each empty box on class 9R's side of stem 1.

   Fill the blanks with these.

   • 4
   • 5
   • 1
   • 7
   • 9
   • 6
   • 2
   • 0
   • 8
   Check

5. 5. The tables show the number of customers a horse-riding school has each day over a two-week period in June and in August. Which back-to-back stem-and-leaf diagram shows this data, with June on the left and August on the right?

   Check

6. 6. The owner of a horse-riding school records the numbers of customers she has each day over two weeks in June and two weeks in August. Work out the mode, median, range and mean for each month.

   • June: mode 46, median 43, range 48, mean 44. August: mode 58, median 51, range 26, mean 49.
   • June: mode 43, median 43, range 48, mean 44. August: mode 58, median 52, range 26, mean 49.
   • June: mode 46, median 46, range 68, mean 44. August: mode 58, median 51, range 62, mean 49.
   • June: mode 46, median 43, range 48, mean 49. August: mode 58, median 51, range 26, mean 44.
   Check

7. 7. The owner of a horse-riding school records the numbers of customers she has each day over two weeks in June and two weeks in August. June: median 43, mean 44, range 48. August: median 51, mean 49, range 26. Which comparison is correct?

   • June had more customers on average (higher median and mean), and its numbers were less spread out.
   • August had more customers on average (higher median and mean), and its numbers were less spread out (smaller range).
   • June had more customers on average, but its numbers were more spread out.
   • August had more customers on average, but its numbers were more spread out (larger range).
   Check

8. 8. The owner of a horse-riding school thinks she has more customers, on average, in August than in June. Do you agree?

   • Yes
   • No
   Check

9. 9. This back-to-back stem-and-leaf diagram shows the times taken by the girls and the boys in a stage 9 class to complete a word puzzle. For each set of times, work out the mode, median, range and mean.

   • Girls: mode 25.5 s, median 26.05 s, range 3 s, mean 26.14 s. Boys: mode 27.7 s, median 27.4 s, range 4 s, mean 27.31 s.
   • Girls: mode 27.3 s, median 26.05 s, range 2.6 s, mean 26.14 s. Boys: mode 26.5 s, median 27.4 s, range 3.6 s, mean 27.31 s.
   • Girls: mode 27.3 s, median 26.1 s, range 2.6 s, mean 26.05 s. Boys: mode 26.5 s, median 27.5 s, range 3.6 s, mean 27.4 s.
   • Girls: mode 26.5 s, median 27.4 s, range 3.6 s, mean 27.31 s. Boys: mode 27.3 s, median 26.05 s, range 2.6 s, mean 26.14 s.
   Check

10. 10. This back-to-back stem-and-leaf diagram shows the times taken by the learners in a stage 9 class to complete a word puzzle. Girls: median 26.05 s, mean 26.14 s, range 2.6 s. Boys: median 27.4 s, mean 27.31 s, range 3.6 s. Which comparison is correct?

    • The girls were quicker on average, but their times were more spread out (larger range).
    • The boys were quicker on average, but their times were more spread out.
    • The boys were quicker on average (lower median and mean), and their times were less spread out.
    • The girls were quicker on average (lower median and mean), and their times were less spread out (smaller range).
    Check

11. 11. This back-to-back stem-and-leaf diagram shows the times taken by the learners in a stage 9 class to complete a word puzzle. Marcus says: 'On average, the boys complete the puzzle more quickly than the girls.' Sofia says: 'On average, the girls complete the puzzle more quickly than the boys.' Which averages are Marcus and Sofia using?

    • Marcus and Sofia are both using the mode.
    • Marcus is using the mode; Sofia is using the median or the mean.
    • Marcus is using the median; Sofia is using the mode.
    • Marcus is using the mean; Sofia is using the mode.
    Check

12. 12. This back-to-back stem-and-leaf diagram shows the times taken by the learners in a stage 9 class to complete a word puzzle. Who do you think completes the puzzle more quickly, the girls or the boys?

    • The boys
    • It is impossible to tell
    • Both the same
    • The girls
    Check

13. 13. The stem-and-leaf diagram shows the mass of potatoes grown per plant for 12 plants in each of two locations. What fraction of the plants from each location had a mass of potatoes less than 700 g per plant?

    • Location A 1/3, location B 1/2
    • Location A 1/4, location B 2/3
    • Location A 1/4, location B 1/4
    • Location A 2/3, location B 1/4
    Check

14. 14. The stem-and-leaf diagram shows the mass of potatoes grown per plant for 12 plants in each of two locations. What percentage of the plants from each location had a mass of potatoes greater than 825 g per plant?

    • Location A 33⅓%, location B 0%
    • Location A 0%, location B 33⅓%
    • Location A 41⅔%, location B 0%
    • Location A 33⅓%, location B 16⅔%
    Check

15. 15. The stem-and-leaf diagram shows the mass of potatoes grown per plant for 12 plants in each of two locations. Which location had the most variation in the mass of potatoes grown per plant?

    • It is impossible to tell
    • Location B
    • Both the same
    • Location A
    Check

16. 16. The stem-and-leaf diagram shows the mass of potatoes grown per plant for 12 plants in each of two locations. What are the mean and median mass of potatoes per plant for each location?

    • A: mean 658.3 g, median 652.5 g. B: mean 792.5 g, median 790 g.
    • A: mean 790 g, median 792.5 g. B: mean 652.5 g, median 658.3 g.
    • A: mean 792.5 g, median 790 g. B: mean 658.3 g, median 652.5 g.
    • A: mean 792.5 g, median 782.5 g. B: mean 658.3 g, median 630 g.
    Check

17. 17. The stem-and-leaf diagram shows the mass of potatoes grown per plant for 12 plants in each of two locations. Which location do you think has the better conditions for growing potatoes?

    • Location B
    • Both the same
    • Location A
    • It is impossible to tell
    Check

18. 18. The tables show the number of boxes of cereal sold in a supermarket each day over a two-week period, when the cereal was on the top shelf and on the middle shelf. Which back-to-back stem-and-leaf diagram shows this data, with the top shelf on the left?

    Check

19. 19. The tables show the number of boxes of cereal sold in a supermarket each day over a two-week period, when the cereal was on the top shelf and on the middle shelf. Do you think sales of the cereal were better when it was on the top shelf or on the middle shelf?

    • The middle shelf
    • Both the same
    • The top shelf
    • It is impossible to tell
    Check

20. 20. Oditi compares the heights of the learners in classes 9T and 9R. She draws this back-to-back stem-and-leaf diagram and works out the range, median, mode and mean for each class. Unfortunately she has spilt tea on her work! Work out the numbers under the tea stains in the table: drag a number into each empty box.

    Fill the blanks with these.

    • 149
    • 147
    • 145
    • 152
    • 144
    Check