Stage 8 - Q1 - 2 marks
A time of exactly 10 minutes is assigned to \(0\le t<10\) or \(10\le t<20\). Which class is correct?
Hint
Check which inequality allows equality.
Stage 8 - Q2 - 2 marks
How many journeys lasted at least twenty but less than thirty minutes?
Hint
Use the full interval, not one endpoint.
Stage 8 - Q3 - 2 marks
How many journeys lasted at least twenty minutes?
Hint
Every time in the final two classes qualifies.
Stage 8 - Q4 - 2 marks
Find the total number of journeys represented.
Hint
Sum all class frequencies.
Stage 8 - Q5 - 3 marks
What fraction of journeys lasted less than twenty minutes?
Hint
Keep the strict upper boundary in mind.
Stage 8 - Q6 - 4 marks
Draw a continuous frequency diagram for \(0\le t<5\), \(5\le t<10\), \(10\le t<15\), \(15\le t<20\), with frequencies 3, 5, 9, 7.
Hint
Continuous intervals are adjacent, so the bars touch.
Stage 8 - Q7 - 4 marks
Four equal-width intervals have frequencies 4, 7, x, 5. Thirty observations were collected. Find x and the fraction in the third interval.
Hint
The missing class completes the full sample.
Stage 8 - Q8 - 4 marks
A table stops at \(30\le t<40\). A new observation is exactly forty minutes. May it be placed in that last class? State a suitable additional class.
Hint
A measurement must not be forced into an interval that excludes it.
Stage 8 - Q9 - 5 marks
Two observations lie in \(0\le t<10\) and two in \(10\le t<20\). Give two possible data sets with different exact means but the same grouped frequencies.
Hint
Move observations within their permitted intervals.
Stage 8 - Q10 - 6 marks
Twenty times have frequencies 6, 7, 7 in \(0\le t<10\), \(10\le t<20\), \(20\le t<30\). Locate the median’s interval. Then find the smallest and largest possible number of times that are at least fifteen minutes.
Hint
Separate what is certain from what could happen inside the middle interval.