Answer :
Final answer:
The 68-95-99.7 rule, or the Empirical Rule, can be used to estimate the percentage of data within different standard deviations from the mean. However, certain assumptions must be made about the data before applying this rule.
Explanation:
The 68-95-99.7 rule, also known as the Empirical Rule, is a statistical rule that applies to data with a bell-shaped and symmetric distribution. Before using this rule, there are important assumptions that must be made about the data:
1. The data follows a bell-shaped and symmetric distribution: A bell-shaped distribution is also known as a normal distribution, where the data is symmetrically distributed around the mean. This means that the curve can be folded along a line of symmetry drawn through the median.
2. The data is representative of the population: In order for the rule to accurately estimate the percentage of data within a certain range, it is important that the data is a representative sample of the entire population.
3. The data is independent and randomly collected: The rule assumes that each data point is collected independently and randomly, without any bias or influence from external factors.
By making these assumptions, we can confidently use the 68-95-99.7 rule to estimate the percentage of data within different standard deviations from the mean.
