What accounts for a difference between the median age of 45 and mean age of 55 in a diabetes intervention program study?

• A. The subjects were predominantly younger than 45
• B. The sample included subjects older than the age of 45
• C. Calculation errors occurred in the study
• D. The study had equal age representation

Answer: (B)

The difference between the median age of 45 and the mean age of 55 can be attributed to the presence of subjects older than age 45 in the sample. The median is the middle value when all ages are arranged in order, so a median of 45 indicates that half of the participants are younger and half are older than this age. The mean age, being higher at 55, suggests that there is a substantial number of individuals who are older than 55 contributing to the average.

This skewing effect can occur if the ages of some participants are significantly high, which would pull the mean up while not affecting the median as dramatically. If the sample contained mostly younger participants but with a few outliers who are much older, this explanation aligns perfectly with the observed numerical values of the median and mean. Thus, incorporating participants older than 45 leads to a situation where the mean is influenced more than the median, resulting in the observed difference.