Mathematics
Mathematics
Problem
A survey plotted ‘less than’ ogives for monthly family income in two towns, P and Q. The curves show the following points: • Town P: 40 % of families earn below Rs 12,000 and 60 % earn below Rs 18,000. • Town Q: 40 % of families earn below Rs 10,000 and 60 % earn below Rs 20,000. Which comparison is correct? a) Town P has a higher median and lower variability than Town Q b) Town Q has a higher median and lower variability than Town P c) Both towns have the same median, but Town Q shows greater variability d) Both towns have the same median and the same variabilityIntuitive explanation
A 'less than' ogive plots cumulative percentage against income, letting you read off what fraction of families fall below any given threshold. The key insight is that the spread of an ogive reveals income inequality: a steep curve means incomes cluster tightly, while a gentle curve means they're spread out. By comparing how the two towns' curves progress from 40% to 60%, you can see which town has more compressed or dispersed earnings—and thus infer which has greater income inequality or a higher median income.
Intuitive explanation
A 'less than' ogive plots cumulative percentage against income, letting you read off what fraction of families fall below any given threshold. The key insight is that the spread of an ogive reveals income inequality: a steep curve means incomes cluster tightly, while a gentle curve means they're spread out. By comparing how the two towns' curves progress from 40% to 60%, you can see which town has more compressed or dispersed earnings—and thus infer which has greater income inequality or a higher median income.