Stage 9 - Q1 - 4 marks
Use the outer occupied class boundaries to estimate the range. Explain why it is not the actual attained range.
Hint
An empty end class contains no possible extreme observation.
Stage 9 - Q2 - 5 marks
Estimate the mean time to 1 decimal place. Show midpoint products and explain why the answer is an estimate.
Hint
Every class midpoint is repeated as many times as its frequency.
Stage 9 - Q3 - 5 marks
Estimate the mean to 1 decimal place and the range from occupied outer class boundaries. Label both answers as estimates.
Hint
The mean uses every frequency; the range estimate uses the occupied extremes.
Stage 9 - Q4 - 4 marks
Estimate the combined time for all observations, then the mean time. Give the mean to 1 decimal place.
Hint
Do not divide until the question asks for a mean.
Stage 9 - Q5 - 4 marks
A pupil averages the five class midpoints and reports \(40\) minutes. Explain the flaw and calculate the correct estimated mean.
Hint
A class with twenty observations must count more than a class with two.
Stage 9 - Q6 - 5 marks
Compare the two estimated mean times to 1 decimal place using matching class midpoints.
Hint
Use the same midpoints but different frequencies.
Stage 9 - Q7 - 5 marks
The midpoint estimate of the mean is exactly 30 minutes. Find the missing frequency in the table.
Hint
The unknown frequency changes the total number of observations as well as the total midpoint products.
Stage 9 - Q8 - 5 marks
Compare the two estimated mean times to 1 decimal place using matching class midpoints.
Hint
Use the same midpoints but different frequencies.
Stage 9 - Q9 - 5 marks
The midpoint estimate of the mean is exactly 25 minutes. Find the missing frequency in the table.
Hint
The unknown frequency changes the total number of observations as well as the total midpoint products.
Stage 9 - Q10 - 7 marks
Times in minutes are grouped as \(0\le t<10\), \(10\le t<20\), \(20\le t<30\) with frequencies 2,3,5. Find the midpoint mean estimate and the tight interval guaranteed to contain the true mean. Can the estimate be above or below the true mean?
Hint
Replace every hidden value by its class lower bound, then by its upper bound, to bound the total.