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

Questions

1. 1. The table shows the times taken by the 31 students in class 9G to complete a cross-country run. Which gives the modal class interval and the class interval where the median lies?

   • modal class 10 ≤ t < 12; median in 12 ≤ t < 14
   • modal class 12 ≤ t < 14; median in 12 ≤ t < 14
   • modal class 14 ≤ t < 16; median in 14 ≤ t < 16
   • modal class 12 ≤ t < 14; median in 14 ≤ t < 16
   Check

2. 2. The table shows the times taken by the 31 students in class 9G to complete a cross-country run. What is an estimate of the range?

   • 10 minutes
   • 8 minutes
   • 18 minutes
   • 6 minutes
   Check

3. 3. Copy and complete the table and workings to find an estimate of the mean time. Put each number in its box. Give the mean correct to the nearest minute.

   Fill the blanks with these.

   • 417
   • 36
   • 15
   • 17
   • 150
   • 13
   • 156
   • 34
   • 14
   Check

4. 4. Why are an estimate of the range and an estimate of the mean worked out from grouped data only estimates?

   • They aren't estimates; they are exact.
   • You don't know the exact values, only which class each one is in.
   • Because you divide by the number of classes.
   • Because the frequencies are rounded.
   Check

5. 5. The table shows the heights of 20 pear trees. Which gives the modal class interval and the class interval where the median lies?

   • modal class 310 ≤ h < 330; median in 270 ≤ h < 290
   • modal class 290 ≤ h < 310; median in 270 ≤ h < 290
   • modal class 270 ≤ h < 290; median in 290 ≤ h < 310
   • modal class 290 ≤ h < 310; median in 290 ≤ h < 310
   Check

6. 6. The table shows the heights of 20 pear trees. Why can you only give class intervals for the mode and the median, and not exact values?

   • The exact heights aren't known, only how many are in each class.
   • Because the median is always a midpoint.
   • Because the classes are different sizes.
   • Because there is an even number of trees.
   Check

7. 7. The table shows the heights of 20 pear trees. What are an estimate of the range and an estimate of the mean height?

   • range 80 cm, mean 300 cm
   • range 330 cm, mean 280 cm
   • range 60 cm, mean 290 cm
   • range 80 cm, mean 290 cm
   Check

8. 8. The table shows the ages of the competitors in a marathon. How many men and how many women ran?

   • 150 men and 140 women
   • 290 men and 140 women
   • 140 men and 150 women
   • 150 men and 150 women
   Check

9. 9. The table shows the ages of the competitors in a marathon. Which row gives the modal class interval, the class interval where the median lies and the estimate of the mean (modal class, median class, mean)?

   • Men: 20–30, 30–40, 39.6. Women: 50–60, 30–40, 42.5
   • Men: 20–30, 40–50, 39.6. Women: 50–60, 40–50, 42.5
   • Men: 20–30, 40–50, 42.5. Women: 50–60, 40–50, 39.6
   • Men: 40–50, 40–50, 39.6. Women: 40–50, 40–50, 42.5
   Check

10. 10. The table shows the ages of the competitors in a marathon. Which comment about the average age of the competitors is correct?

    • The men's and women's estimated mean ages are the same.
    • The women's estimated mean age is about 10 years higher than the men's.
    • The men's estimated mean age is about 3 years higher than the women's.
    • The women's estimated mean age is about 3 years higher than the men's.
    Check

11. 11. The table shows the ages of the competitors in a marathon. On average, who are the younger competitors, the men or the women?

    • the women
    • the men
    • They are the same.
    • You can't tell from means.
    Check

12. 12. Fabio records the number of text messages he sends each day for 20 days. What are the mean, median and mode of his results?

    • mean 15.5, median 15.6, mode 8
    • mean 15.6, median 14.5, mode 19
    • mean 15.6, median 15.5, mode 8
    • mean 15.6, median 15.5, mode 12
    Check

13. 13. Fabio records the number of text messages he sends each day for 20 days. He groups the data in two frequency tables. Put each frequency in its box.

    Fill the blanks with these.

    • 7
    • 5
    • 4
    • 10
    • 2
    • 6
    • 3
    • 8
    • 9
    Check

14. 14. Fabio's two frequency tables are shown. Which row gives the modal class interval, the class interval where the median lies and the estimate of the mean for each table?

    • Table A: 12–18, 12–18, 15.75. Table B: 14–22, 14–22, 16.05
    • Table A: 5–11, 12–18, 16.05. Table B: 14–22, 14–22, 15.75
    • Table A: 12–18, 12–18, 16.05. Table B: 5–13, 14–22, 15.75
    • Table A: 12–18, 12–18, 16.05. Table B: 14–22, 14–22, 15.75
    Check

15. 15. The accurate mean, median and mode are 15.6, 15.5 and 8. Fabio's estimates of the mean are 16.05 (Table A) and 15.75 (Table B); his median class intervals are 12–18 and 14–22; his modal class intervals are 12–18 and 14–22. What do you notice?

    • Table A's mean estimate is closer to 15.6, the median is outside both intervals, and the mode is in neither modal class.
    • Both mean estimates are exactly 15.6, the median is inside both intervals, and the mode is in both modal classes.
    • Both mean estimates are close to 15.6 (Table B''s is closer), the median is inside both intervals, and the mode is in neither modal class.
    • Both mean estimates are far from 15.6, the median is inside both intervals, and the mode is in both modal classes.
    Check

16. 16. The table shows the ages of the people watching a rugby match. Which gives the modal class interval and the class interval where the median lies?

    • modal class 10 < a ≤ 20; median in 30 < a ≤ 40
    • modal class 40 < a ≤ 50; median in 30 < a ≤ 40
    • modal class 40 < a ≤ 50; median in 20 < a ≤ 30
    • modal class 30 < a ≤ 40; median in 40 < a ≤ 50
    Check

17. 17. The table shows the ages of the people watching a rugby match. What are an estimate of the mean age and an estimate of the range?

    • mean 36.2 years, range 70 years
    • mean 36.2 years, range 80 years
    • mean 37.1 years, range 80 years
    • mean 40 years, range 75 years
    Check

18. 18. The table shows the ages of the people watching a rugby match. Henri regroups the data into classes 0 < a ≤ 20, 20 < a ≤ 40, 40 < a ≤ 60 and 60 < a ≤ 80. What are the four frequencies, in order?

    • 13, 14, 12, 8
    • 13, 8, 12, 8
    • 13, 8, 10, 8
    • 18, 8, 12, 8
    Check

19. 19. Henri regrouped the ages into classes 0 < a ≤ 20, 20 < a ≤ 40, 40 < a ≤ 60 and 60 < a ≤ 80; his table is shown. Which gives the modal class interval and the class interval where the median lies?

    • modal class 20 < a ≤ 40; median in 20 < a ≤ 40
    • modal class 40 < a ≤ 60; median in 40 < a ≤ 60
    • modal class 0 < a ≤ 20; median in 20 < a ≤ 40
    • modal class 40 < a ≤ 60; median in 20 < a ≤ 40
    Check

20. 20. Henri regrouped the ages into classes 0 < a ≤ 20, 20 < a ≤ 40, 40 < a ≤ 60 and 60 < a ≤ 80; his table is shown. What are an estimate of the mean age and an estimate of the range?

    • mean 37.3 years, range 80 years
    • mean 36.2 years, range 80 years
    • mean 40 years, range 70 years
    • mean 37.3 years, range 60 years
    Check