Question

As part of its twenty-fifth reunion celebration, the Class of 1980 of State University mailed a questionnaire to its members. One of the questions asked the respondent to give his or her total income last year. Of the 820 members of the class of 1980, the university alumni office had addresses for 583. Of these, 421 returned the questionnaire. The reunion committee computed the mean income given in the responses and announced, ”The members of the class of 1980 have enjoyed resounding success. The average income of class members is $120,000!”. Identify two distinct sources of misleading information in this result, being explicit about the direction of the mistake you expect. Explain how you might fix each of these problems.

Answer 1

Distinct source of misleading information in this result 1:

The reunion committee computed the mean income given in the responses. Since the distribution of income of the members is highly skewed with some members having very high income and some members having very low income, mean is not appropriate measure of central tendency and only median is appropriate measure of central tendency because mean is affected by extreme values whereas median is not affected by extreme values.

Distinct source of misleading information in this result 2:

The survey has Response Bias as follows. Since the survey is open, if a member has very low incme, he may not give the correct information due to social desirability reasons. Similarly a high income member may not reveal his high income because of fear of being known to Income Tax personnel.

Problem 1 is fixed by using median in place of mean.

Problem 2 is fixed by making the survey confidential, hiding the identity of the members so that all the members will give their exact income without any fear of being noted by others.