Answer :
The 68-95-99.7 Rule, also known as the empirical rule, is a statistical guideline for normal distributions. In this rule, the significance of the number 95 is explained as follows:
1. Normal Distribution: This rule applies to bell-shaped curves where data is symmetrically distributed around the mean.
2. Standard Deviations: In statistics, standard deviation measures the amount of variation or dispersion in a set of values. In a normal distribution:
- The mean is at the center of the distribution.
3. The 68-95-99.7 Rule: This states:
- 68% of the data falls within one standard deviation of the mean. This means that if you move one standard deviation away from the mean in both directions (left and right), you'll find about 68% of the dataset.
- 95% of the data falls within two standard deviations of the mean. Therefore, moving two standard deviations away from the mean in both directions covers approximately 95% of the dataset.
- 99.7% of the data falls within three standard deviations of the mean, representing almost all of the data in the dataset.
The number 95 is significant because it provides a measure of data spread where most observations can be found within that range around the mean—specifically from two standard deviations below the mean to two standard deviations above the mean. This forms the basis for the calculation of a 95% confidence interval, which is used to infer the population parameter with a certain level of confidence.
1. Normal Distribution: This rule applies to bell-shaped curves where data is symmetrically distributed around the mean.
2. Standard Deviations: In statistics, standard deviation measures the amount of variation or dispersion in a set of values. In a normal distribution:
- The mean is at the center of the distribution.
3. The 68-95-99.7 Rule: This states:
- 68% of the data falls within one standard deviation of the mean. This means that if you move one standard deviation away from the mean in both directions (left and right), you'll find about 68% of the dataset.
- 95% of the data falls within two standard deviations of the mean. Therefore, moving two standard deviations away from the mean in both directions covers approximately 95% of the dataset.
- 99.7% of the data falls within three standard deviations of the mean, representing almost all of the data in the dataset.
The number 95 is significant because it provides a measure of data spread where most observations can be found within that range around the mean—specifically from two standard deviations below the mean to two standard deviations above the mean. This forms the basis for the calculation of a 95% confidence interval, which is used to infer the population parameter with a certain level of confidence.
