Stage 8 - Q1 - 2 marks
Favourite colours are red, blue, blue, green, blue. Which average is meaningful for the most popular colour?
Hint
The question asks for the most frequent category.
Stage 8 - Q2 - 2 marks
Find the mode of shoe sizes 4, 5, 5, 6, 7.
Hint
Find the most frequent value.
Stage 8 - Q3 - 3 marks
Waits are 2, 3, 3, 4, 28 minutes. Find mean and median and select a reasonable summary of a usual wait.
Hint
Consider the effect of the extreme value.
Stage 8 - Q4 - 3 marks
A cafe sells five meals at costs 4, 5, 5, 6, 10 USD. Which average helps recover total cost, and what is that average?
Hint
The task concerns a total spread across all items.
Stage 8 - Q5 - 4 marks
The data are 1, 2, 3, 4, 5. Is there a unique mode? Explain, and give the median.
Hint
A mode must be determined by frequency.
Stage 8 - Q6 - 4 marks
Two sets have mean 10: A=(9, 10, 10, 10, 11), B=(0, 5, 10, 15, 20). Which is more consistent by range? Can the mean alone reveal that?
Hint
Use a spread statistic as well as an average.
Stage 8 - Q7 - 4 marks
Six pupils have mean score 12 and four pupils have mean score 17. Find the combined mean.
Hint
Weight each mean by its group size.
Stage 8 - Q8 - 4 marks
A manager reports the mean salary of 4, 4, 4, 4, 24 thousand units as 8 thousand. Another reports median 4 thousand. Are either calculations wrong? Which better describes a typical worker here?
Hint
A difference between averages need not be an error.
Stage 8 - Q9 - 5 marks
A group of eight has mean 15. After two people join, the mean is 16. Their scores differ by 4. Find the two new scores.
Hint
Recover the added total before using the difference.
Stage 8 - Q10 - 6 marks
Construct two five-value nonnegative integer data sets so A has a higher mean but a lower median than B. Show both comparisons and explain why “A did better on average” needs the chosen average to be named.
Hint
Use one large value to raise a mean while keeping most observations small.