Stage 9 - Q1 - 4 marks
Two equal-sized samples record completion time. Compare how many times are at least 50 minutes. Which sample has more slower completions by this criterion?
Hint
Use the two vertices whose classes start at or above the threshold.
Stage 9 - Q2 - 4 marks
Two equal-sized samples record completion time. Compare how many times are at least 50 minutes. Which sample has more slower completions by this criterion?
Hint
Use the two vertices whose classes start at or above the threshold.
Stage 9 - Q3 - 4 marks
The samples have equal size. Compare their occupied spans using the polygons, and explain the limit of this spread comparison.
Hint
Distinguish occupied class boundaries from attained minimum and maximum values.
Stage 9 - Q4 - 3 marks
For the same score class, sample A has frequency 44 out of 110; sample B has frequency 66 out of 220. Which has the larger proportion in that class?
Hint
Use each sample total as its denominator.
Stage 9 - Q5 - 4 marks
The two polygons have frequencies B exactly twice A in every class. Does the taller B polygon prove larger typical values? Explain.
Hint
Compare proportions, not raw counts, when sample sizes differ.
Stage 9 - Q6 - 4 marks
Group A used 5-minute classes and B used 10-minute classes, both starting at 20. A pupil overlays the polygons and compares peaks. How can the data be made comparable without inventing values?
Hint
A larger class can be formed by adding known subgroups.
Stage 9 - Q7 - 4 marks
The samples have equal size. Compare their occupied spans using the polygons, and explain the limit of this spread comparison.
Hint
Distinguish occupied class boundaries from attained minimum and maximum values.
Stage 9 - Q8 - 3 marks
For the same score class, sample A has frequency 36 out of 90; sample B has frequency 54 out of 180. Which has the larger proportion in that class?
Hint
Use each sample total as its denominator.
Stage 9 - Q9 - 4 marks
Group A used 5-minute classes and B used 10-minute classes, both starting at 40. A pupil overlays the polygons and compares peaks. How can the data be made comparable without inventing values?
Hint
A larger class can be formed by adding known subgroups.
Stage 9 - Q10 - 6 marks
A uses 5-minute classes from 0 to 20 with frequencies 3,7,9,1. B uses 10-minute classes from 0 to 20 with frequencies 24,16. Compare the observed proportions below 10 minutes using fair grouping and scaling. Does the larger raw B peak alone establish this conclusion?
Hint
First match interval boundaries, then account for sample totals.