Handling Data 6
4 marks · HardThe histograms below show the distribution of journey times (in minutes) to school for two local schools, Alpha and Beta. Both schools had the same total number of students surveyed.
Compare the two distributions. Give two differences and what they show about the journey times for Alpha and Beta.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Must show: Two valid differences comparing distribution shape or spread, Linked comments about what the differences mean in context
Also accept: Alpha has a higher frequency density in the shortest group, meaning more students at Alpha have very short journey times.; Beta has fewer students with very short journeys, and more students with journey times spread over longer intervals.; Beta has a lower peak but a wider spread, suggesting journey times are more varied.
Common mistakes: Referring only to absolute frequency, not density or spread; Making non-comparative statements
Show mark scheme and worked solution
Marking points
B1 · 1 mark · Identifies a correct difference in modal class or peak between Alpha and Beta
B2 · 1 mark · Explains what this difference shows about journey times
B3 · 1 mark · Identifies a second, different and correct feature (such as spread or skewness)
B4 · 1 mark · Explains what this second difference shows about journey times
Worked solution
Alpha's histogram has the highest frequency density in the shortest time group (0–10 minutes), meaning more students from Alpha have short journey times, while Beta's highest frequency density is lower and spread between 0–15 minutes.
Secondly, Beta's journey times are more spread out across longer intervals, suggesting times are more varied for Beta students, whereas Alpha has a larger group with short journey times.