The mean DMFT values for 12 year old school children is 2.5. 68% of the population has DMFT values between 2 and 3. The standard deviation for the population is:
## Core Concept
The problem involves understanding the relationship between the mean, standard deviation, and the distribution of DMFT (Decayed, Missing, and Filled Teeth) values in a population of 12-year-old school children. Specifically, it tests the application of statistical concepts, particularly the 68-95-99.7 rule, also known as the empirical rule.
## Why the Correct Answer is Right
The empirical rule states that about 68% of the data falls within one standard deviation of the mean. Given that the mean DMFT value is 2.5 and 68% of the population has DMFT values between 2 and 3, this implies that the range from 2 to 3 encompasses one standard deviation on either side of the mean. Therefore, the distance from the mean to either 2 or 3 represents one standard deviation. Since 2.5 is the mean, and it is equidistant from 2 and 3, we can calculate the standard deviation as follows:
- The distance from 2.5 to 2 is 0.5.
- The distance from 2.5 to 3 is 0.5.
Thus, the standard deviation (σ) is 0.5.
## Why Each Wrong Option is Incorrect
- **Option A:** This option is incorrect because it does not match the calculation based on the information provided.
- **Option B:** This option suggests a standard deviation of 0.1, which does not align with the range provided (between 2 and 3) as being within one standard deviation of the mean.
- **Option D:** This option suggests a standard deviation of 1, which would imply a much wider range for 68% of the population than what is given.
## Clinical Pearl / High-Yield Fact
A key point to remember is the 68-95-99.7 rule, which can help in quickly estimating the standard deviation and understanding the distribution of data in a population. This rule can be particularly useful in epidemiology and biostatistics.
## Correct Answer Line
**Correct Answer: C. 0.5**