A survey records household income only in the classes £0–£20 000, £20 000–£40 000, £40 000–£60 000 and “£60 000 or more”. The researcher uses £70 000 as the midpoint of the final class.
Explain why the resulting estimated mean is especially model-dependent.
Explain why the median may be a more stable summary for these data.
Suggest a refinement that would allow a more defensible estimate of the mean.