Standard deviation is a measure of how dispersed data points are from the average value. It is calculated by taking the square root of the variance, which is the average of the squared distances from the mean. For a set of egg weights, the standard deviation is calculated by first finding the mean, then determining the variance by taking the sum of the squared differences from the mean. A low standard deviation means values are close to the mean, while a high standard deviation means values are more spread out. Standard deviation is not affected by adding or subtracting a constant from all values, but is affected by multiplying or dividing all values by a constant.