Standard deviation is equal to 0 if all values are equal (because all values are then equal to the mean).For two data sets with the same mean, the one with the larger standard deviation is the one in which the data is more spread out from the center.A single very extreme value can increase the standard deviation and misrepresent the dispersion.
Standard deviation is sensitive to extreme values.Remember the following properties when you are using the standard deviation: This is why, in most situations, it is helpful to assess the size of the standard deviation relative to its mean. For example, a measure of two large companies with a difference of $10,000 in annual revenues is considered pretty close, while the measure of two individuals with a weight difference of 30 kilograms is considered far apart. When you are measuring something that is in the scale of millions, having measures that are close to the mean value doesn’t have the same meaning as when you are measuring something that is in the scale of hundreds. The magnitude of the mean value of the dataset affects the interpretation of its standard deviation. Standard deviation might be difficult to interpret in terms of how large it has to be when considering the data to be widely dispersed. A single extreme value can have a big impact on the standard deviation. However, standard deviation is affected by extreme values. An item selected at random from a data set whose standard deviation is low has a better chance of being close to the mean than an item from a data set whose standard deviation is higher. The data set with the smaller standard deviation has a narrower spread of measurements around the mean and therefore usually has comparatively fewer high or low values. Standard deviation is useful when comparing the spread of two separate data sets that have approximately the same mean.
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