What is a low variance?
A variance of zero indicates that all of the data values are identical. All non-zero variances are positive. A small variance indicates that the data points tend to be very close to the mean, and to each other. Variance is the average of the squared distances from each point to the mean.
What information does the standard deviation tell you?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.
What do the mean and standard deviation tell you about a data set?
More precisely, it is a measure of the average distance between the values of the data in the set and the mean. A low standard deviation indicates that the data points tend to be very close to the mean; a high standard deviation indicates that the data points are spread out over a large range of values.