A histogram with a normal distribution has the smallest standard deviation. This is because the normal distribution is the most symmetrical and consistent of all distributions, meaning that its data points are clustered around the mean, with few extreme values. The standard deviation is a measure of how spread out the data points in a distribution are, and the normal distribution has the smallest standard deviation of all distributions.

What distribution has the smallest standard deviation?

The normal distribution has the smallest standard deviation amongst all continuous distributions. The standard deviation for a normal distribution is given by the formula σ = √((μ – μ2)/N), where μ is the mean and N is the number of data points.

How do you find the smallest standard deviation?

The smallest standard deviation is found by calculating the variance of a set of values and then taking the square root of the variance. To calculate the variance, you can use the following formula:

«`
Variance = (∑(x_i — μ)^2)/n
«`

Where x_i is each data point, μ is the mean of the data set, and n is the number of data points. Once you have the variance, you can take the square root of it to get the standard deviation.