**Core Concept**
The secondary attack rate is a measure of the contagiousness of an infectious disease, calculated as the number of cases occurring among contacts within a specified period after exposure to the primary case.

**Why the Correct Answer is Right**
The secondary attack rate of measles is indeed higher than that of mumps. This is because measles is a highly contagious viral infection that spreads through respiratory droplets, aerosolized virus, and direct contact with an infected person. The measles virus has an extremely short incubation period, typically 10-14 days, allowing for rapid spread within a susceptible population. In contrast, mumps has a longer incubation period, which may reduce its contagiousness.

**Why Each Wrong Option is Incorrect**
**Option A:** "Measles is more dangerous than mumps" - While measles can have severe complications, such as encephalitis and pneumonia, the question focuses on infectiousness, not disease severity.

**Option B:** "Mumps is more dangerous than measles" - This statement is not supported by the context of the question, which compares secondary attack rates.

**Option D:** "Measles is more common than mumps" - The question specifically asks about infectiousness, not prevalence or incidence.

**Clinical Pearl / High-Yield Fact**
A high secondary attack rate is often indicative of a highly infectious disease, which may require more stringent public health measures, such as vaccination campaigns and contact tracing.

**Correct Answer Line**
✓ Correct Answer: C. Measles is more infectious than mumps.