Year 9 Maths • AC9M9ST03 • Authored homework
Comparing Data Distributions
Represent and compare multiple numerical data sets using measures of centre, spread and shape. Use dot plots, box plots, histograms or summary statistics to justify comparisons. Show working, use correct statistical language, and justify conclusions.
Part A
Short-answer questions
What is a distribution in statistics?
What does the median tell you about a data set?
What does the mean tell you about a data set?
What does range measure?
What does interquartile range measure?
Why can an outlier affect the mean more than the median?
Name one graph that can compare two numerical data sets.
What does spread mean when comparing data?
What does overlap between two distributions suggest?
Correct this misconception: “The higher mean always means every value is higher.”
Part B
Long-answer questions
Two classes have test-score medians of 68 and 72. Explain why you still need spread information before judging performance.
Create two small data sets with the same mean but different ranges. Explain what this shows.
Compare two data sets using median and interquartile range rather than only the mean.
A data set has one very large outlier. Explain how the mean, median and range are affected.
Describe how a box plot can show median, quartiles, range and possible outliers.
A sports coach compares sprint times for two teams. Explain which team is more consistent using spread.
Interpret a pair of overlapping distributions and explain why conclusions should be cautious.
Choose the best graph to compare two sets of reaction-time data and justify your choice.
Write a comparison paragraph for two data sets, including centre, spread, shape and outliers.
Design a small investigation that collects two numerical data sets and explain how you would compare their distributions.
Part C
Research and understanding task
Collect or invent two related numerical data sets, such as screen time for two groups or reaction times before and after practice. Display both sets and compare centre, spread and any outliers.