Stage 8 - Q1 - 2 marks
Read the smallest journey time.
Hint
Combine the first stem with its first ordered leaf.
Stage 8 - Q2 - 2 marks
Find the modal journey time.
Hint
Look for the most frequent complete value.
Stage 8 - Q3 - 2 marks
Find the range of the journey times.
Hint
Use the full largest and smallest values.
Stage 8 - Q4 - 2 marks
Find the median journey time.
Hint
Count leaves across all stems in order.
Stage 8 - Q5 - 3 marks
What percentage of times exceed 25 minutes?
Hint
Do not include a value merely because it is in the twenties row.
Stage 8 - Q6 - 3 marks
What fraction of the times are at least 18 minutes?
Hint
The phrase “at least” includes equality.
Stage 8 - Q7 - 4 marks
Find the mean journey time.
Hint
A leaf alone is not a data value.
Stage 8 - Q8 - 4 marks
Remove the 40-minute observation. Find the new median and range.
Hint
Both the number of observations and the largest value change.
Stage 8 - Q9 - 5 marks
A pupil finds a mean within each stem row and then averages those four row means equally. Explain why this is unreliable and state the correct mean.
Hint
A row mean must be weighted by its number of observations.
Stage 8 - Q10 - 6 marks
An ordered diagram has values 16, 19,\(20+a\),\(20+b\), 28, 30, where a and b are digits with \(a\le b\). The mean is 23. Find every possible pair of missing leaves and show that the median is fixed.
Hint
Use the mean to constrain the leaf sum before listing possibilities.