A range of two standard deviations on either side of the mean covers what percentage of observations?

A range of two standard deviations on either side of the mean covers what percentage of observations?

• A. 68%
• B. 75%
• C. 90%
• D. 95%

Answer: (D)

The correct response pertains to the empirical rule, also known as the 68-95-99.7 rule, which is fundamental in understanding the distribution of data in a normal distribution. According to this rule, approximately 68% of the observations fall within one standard deviation of the mean, around 95% fall within two standard deviations, and about 99.7% fall within three standard deviations. When focusing on a range of two standard deviations on either side of the mean, it captures a significant majority of the data points within a normal distribution, specifically around 95%. This is crucial for statistical analysis as it provides a clear understanding of where most of the values lie relative to the average, allowing analysts to make inferences about the overall dataset. Understanding the empirical rule allows researchers and analysts to predict probabilities, assess variability, and make informed decisions based on the distribution of the data being analyzed. Thus, recognizing that two standard deviations from the mean encompass approximately 95% of the observations is essential in statistics.

The correct response pertains to the empirical rule, also known as the 68-95-99.7 rule, which is fundamental in understanding the distribution of data in a normal distribution. According to this rule, approximately 68% of the observations fall within one standard deviation of the mean, around 95% fall within two standard deviations, and about 99.7% fall within three standard deviations.

When focusing on a range of two standard deviations on either side of the mean, it captures a significant majority of the data points within a normal distribution, specifically around 95%. This is crucial for statistical analysis as it provides a clear understanding of where most of the values lie relative to the average, allowing analysts to make inferences about the overall dataset.

Understanding the empirical rule allows researchers and analysts to predict probabilities, assess variability, and make informed decisions based on the distribution of the data being analyzed. Thus, recognizing that two standard deviations from the mean encompass approximately 95% of the observations is essential in statistics.