Year 10 Maths • AC9M10ST02 • Authored homework
Boxplots and continuous distributions
Compare distributions using five-number summaries, boxplots, centre, spread, shape, outliers and context.
Part A
Short-answer questions
Name the five values in a five-number summary.
What does the median show in a distribution?
What is the interquartile range and how is it calculated?
If Q1 = 14 and Q3 = 26, find the IQR.
If the minimum is 6 and maximum is 31, find the range.
What does a larger IQR suggest about the middle 50% of the data?
State the common 1.5 IQR rule for identifying potential outliers.
Why are boxplots useful for comparing two or more groups?
What information can a histogram show that a boxplot may hide?
Why should a comparison mention context, not just higher or lower values?
Part B
Long-answer questions
For the data 4, 6, 7, 9, 10, 12, 15, find the median, Q1, Q3, range and IQR. Show your method clearly.
Group A has median 68 and IQR 8. Group B has median 72 and IQR 18. Compare the two groups using centre and spread, then write a context-ready sentence.
For Q1 = 20 and Q3 = 32, calculate the outlier fences using the 1.5 IQR rule. Decide whether 50 is a potential outlier.
A boxplot has a long upper whisker and the median is closer to Q1 than Q3. Describe the likely skew and explain why a histogram could still be useful.
Two classes have similar medians, but Class X has a much smaller IQR. Explain what this suggests about consistency and why this may matter in a school context.
Create a five-number summary for a small continuous dataset of at least 9 values, then describe what the corresponding boxplot would show.
A dataset has one very high value. Explain three possibilities: measurement error, genuine rare value or important subgroup. State how each possibility should be handled.
Compare using range and IQR as measures of spread. Give one situation where IQR gives a better summary than range.
A boxplot comparison shows Group A has lower median waiting time and smaller IQR than Group B. Write a careful conclusion and mention one limitation of using only boxplots.
Choose whether a boxplot, histogram or dot plot would be best for comparing two datasets. Explain your choice based on the statistical question, not just the display type.
Part C
Research and understanding task
Collect or find two small continuous numerical datasets, such as reaction times, heights, waiting times or running times. Create five-number summaries, compare centre and spread, identify any potential outliers, and explain whether a boxplot, histogram or dot plot best communicates the comparison.