How much of a normal distribution falls within 1 standard deviation from the mean?

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. This characteristic of the normal distribution is part of the empirical rule, also known as the 68-95-99.7 rule. The rule states that:

• About 68% of the data lies within one standard deviation (σ) from the mean (μ).

• About 95% of the data is found within two standard deviations.

• About 99.7% of the data lies within three standard deviations.

Thus, when considering the range of values represented by one standard deviation on either side of the mean, it accounts for roughly 68% of the total data set, highlighting the concentration of data around the mean in a normal distribution. This is fundamental in understanding statistical properties and is widely applicable in various fields involving data analysis.