Worksheets · Higher

Cumulative frequency and quantiles

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 2 marks

   The marks of 80 students: $0 < m \le 20$: 4; $20 < m \le 40$: 10; $40 < m \le 60$: 26; $60 < m \le 80$: 30; $80 < m \le 100$: 10.

   (a) Work out the cumulative frequency for marks up to 60. (1)

   (b) Write down the coordinates of the point plotted for the class $40 < m \le 60$ on a cumulative frequency graph. (1)
2. Question 2Non-calculator · 5 marks

   A cumulative-frequency model has points $(0,0)$, $(10,12)$, $(20,60)$, $(30,108)$ and $(40,120)$, joined by straight lines. The horizontal axis is waiting time in minutes.

   (a) Estimate the interquartile range using cumulative frequencies 30 and 90. (3)

   (b) Estimate the number waiting more than 25 minutes. (2)
3. Question 3Non-calculator · 3 marks

   Two schools sat the same test. School $A$: median 60, lower quartile 45, upper quartile 73. School $B$: median 64, lower quartile 58, upper quartile 70.

   (a) Compare the distributions of the marks at the two schools. (3)