What percentage of data falls within one standard deviation in a normal distribution?

What percentage of data falls within one standard deviation in a normal distribution?

• A. 68%
• B. 75%
• C. 80%
• D. 90%

Answer: (A)

In a normal distribution, one of the essential characteristics is how data is spread out around the mean. The empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the data falls within one standard deviation of the mean. This rule exemplifies the tendency of data points to cluster around the average, illustrating that in a perfectly symmetrical bell-shaped curve, most observations reside within that one standard deviation range. Thus, when considering a normal distribution, recognizing that 68% of the data lying within this range indicates the concentration of data around the mean helps to understand one of the fundamental properties of normal distributions and their significance in statistical analysis.

In a normal distribution, one of the essential characteristics is how data is spread out around the mean. The empirical rule, also known as the 68-95-99.7 rule, states that approximately 68% of the data falls within one standard deviation of the mean. This rule exemplifies the tendency of data points to cluster around the average, illustrating that in a perfectly symmetrical bell-shaped curve, most observations reside within that one standard deviation range.

Thus, when considering a normal distribution, recognizing that 68% of the data lying within this range indicates the concentration of data around the mean helps to understand one of the fundamental properties of normal distributions and their significance in statistical analysis.