What percentage of data falls within 3 standard deviations?

• A. 68% of data
• B. 99.7% of data
• C. 95% of data
• D. 100% of data

Answer: (B)

In a normal distribution, most data cluster near the mean and standard deviation measures how far observations tend to spread. The empirical rule, often called the 68-95-99.7 rule, tells us the percentages of data within certain distances from the mean: about 68% lie within one standard deviation, about 95% within two, and about 99.7% within three. So the data within three standard deviations amount to roughly 99.7%. This is a good approximation for bell-shaped data; real data can deviate a bit, but this rule is a handy guideline. The other options correspond to smaller ranges or to the idea that all data must lie within a fixed number of standard deviations, which isn’t the case in practice because of possible outliers.