In a symmetrical bell curve, what does a larger standard deviation indicate?

In a symmetrical bell curve, what does a larger standard deviation indicate?

• A. The data is more spread out
• B. The data is more tightly clustered
• C. The mean is higher
• D. The sample size is larger

Answer: (A)

Standard deviation measures how far data tend to lie from the mean. In a normal bell curve, a larger standard deviation makes the curve wider and flatter because observations are more spread out around the mean. This increased dispersion is what “more spread out” means. The mean is a location parameter, so raising the standard deviation doesn’t imply a higher mean, and standard deviation reflects variability rather than sample size. So the data are more spread out.

Standard deviation measures how far data tend to lie from the mean. In a normal bell curve, a larger standard deviation makes the curve wider and flatter because observations are more spread out around the mean. This increased dispersion is what “more spread out” means. The mean is a location parameter, so raising the standard deviation doesn’t imply a higher mean, and standard deviation reflects variability rather than sample size. So the data are more spread out.