What percentage of the population falls within one standard deviation of the mean?

The question pertains to the concept of the normal distribution, also known as the bell curve, which is a fundamental statistical concept. In a perfectly normal distribution, approximately 68% of the data points lie within one standard deviation (±1σ) of the mean (μ). This is a crucial concept in statistics as it helps to understand how data is distributed around the mean.

The significance of this percentage is paramount when interpreting data, as it indicates where the majority of observations can be expected to fall. Knowing that about two-thirds of the population lies within this range aids in making predictions and assessing how extreme or typical a specific data point is relative to the average.

In contrast, the other percentages listed correspond to differing ranges in a normal distribution: approximately 95% of the population falls within two standard deviations of the mean, and about 99% falls within three standard deviations. These values are often used in various fields, including medicine and psychology, when evaluating data sets or when assessing test results, where understanding the spread of data is crucial for effective analysis and decision-making.