What percentage of observations is covered by a range of one standard deviation on either side of the mean?

What percentage of observations is covered by a range of one standard deviation on either side of the mean?

• A. 50%
• B. 68%
• C. 75%
• D. 95%

Answer: (B)

The correct answer is 68%. In a normal distribution, which is a common assumption in statistics for many real-world phenomena, approximately 68% of the observations fall within one standard deviation of the mean. This property is part of the empirical rule, also known as the 68-95-99.7 rule. According to this rule, about 68% of the data points will be within one standard deviation from the mean in both directions (i.e., mean - one standard deviation to mean + one standard deviation). This characteristic of normal distribution helps in understanding how data is spread around the mean and provides a convenient way to assess the likelihood of a data point falling within that range. Other answer choices reflect percentages relating to different ranges within the normal distribution. For instance, 95% of observations fall within two standard deviations of the mean, while three standard deviations encompass approximately 99.7% of the data. Thus, the specific percentage of 68% accurately represents the proportion of data within one standard deviation of the mean in a normal distribution.

The correct answer is 68%. In a normal distribution, which is a common assumption in statistics for many real-world phenomena, approximately 68% of the observations fall within one standard deviation of the mean. This property is part of the empirical rule, also known as the 68-95-99.7 rule.

According to this rule, about 68% of the data points will be within one standard deviation from the mean in both directions (i.e., mean - one standard deviation to mean + one standard deviation). This characteristic of normal distribution helps in understanding how data is spread around the mean and provides a convenient way to assess the likelihood of a data point falling within that range.

Other answer choices reflect percentages relating to different ranges within the normal distribution. For instance, 95% of observations fall within two standard deviations of the mean, while three standard deviations encompass approximately 99.7% of the data. Thus, the specific percentage of 68% accurately represents the proportion of data within one standard deviation of the mean in a normal distribution.