Stage 8 - Q1 - 2 marks
Find the mean of 4, 6, 8.
Hint
Total divided by count.
Stage 8 - Q2 - 2 marks
Find the median of 3, 9, 4, 7, 5.
Hint
Order before taking the middle.
Stage 8 - Q3 - 2 marks
Find the range of 12, 7, 15, 9, 11.
Hint
Use extremes, not the first and last written values.
Stage 8 - Q4 - 2 marks
Compare the mean scores of A=(6, 8, 10, 12) and B=(7, 8, 9, 8).
Hint
Both groups have four observations.
Stage 8 - Q5 - 3 marks
Group A has total score 60 from five pupils. Group B has total score 77 from seven pupils. Which mean is higher?
Hint
Different group sizes make raw totals misleading.
Stage 8 - Q6 - 4 marks
A=(8, 9, 10, 11, 12) and B=(2, 6, 10, 14, 18). Compare their means and ranges.
Hint
Calculate centre and spread separately.
Stage 8 - Q7 - 4 marks
The values 4, 5, 6, 7, 8 gain one extra value, 30. Find the new mean and median. Which changes more?
Hint
Compare with the original mean and median, both six.
Stage 8 - Q8 - 4 marks
Five scores are 8, 11, 12, 14, x and their mean is 12. Find x.
Hint
Mean times count gives the required total.
Stage 8 - Q9 - 5 marks
Four scores have mean 13. A fifth score is added and the mean becomes 14. Find the new score and explain why it must exceed 14.
Hint
Compare the old and new totals.
Stage 8 - Q10 - 6 marks
Create two sets of five nonnegative integers, both with mean 10. The first must have median 6 and the second median 14. Verify all conditions and explain what this shows about the mean.
Hint
Choose the middle value first, then balance the remaining values to make the required total.