For a data value set that is Gaussian distributed, what is the likelihood (%) that a data point will be within ±1 SD from the mean?

For a data value set that is Gaussian distributed, what is the likelihood (%) that a data point will be within ±1 SD from the mean?

• A. 68%
• B. 99%
• C. 95%
• D. 100%

Answer: (A)

In a Gaussian distribution, the spread around the mean is described by the standard deviation, and the empirical rule tells us how data cluster around the center. About 68% of values fall within one standard deviation of the mean, which corresponds to the interval μ ± σ. The exact probability for a standard normal variable is P(-1 ≤ Z ≤ 1) ≈ 0.6827, i.e., 68.27%, so rounding gives roughly 68%. This is the most common benchmark students memorize for this range. For context, about 95% lie within ±2 SD and about 99.7% within ±3 SD.

In a Gaussian distribution, the spread around the mean is described by the standard deviation, and the empirical rule tells us how data cluster around the center. About 68% of values fall within one standard deviation of the mean, which corresponds to the interval μ ± σ. The exact probability for a standard normal variable is P(-1 ≤ Z ≤ 1) ≈ 0.6827, i.e., 68.27%, so rounding gives roughly 68%. This is the most common benchmark students memorize for this range. For context, about 95% lie within ±2 SD and about 99.7% within ±3 SD.