Standard Deviation vs Range

Range captures the difference between the highest and lowest value in a data set, while standard deviation measures the variation of elements from the mean. Range is extremely sensitive to outliers, it tells us almost nothing about the distribution of the data, and does not extrapolate to new data (a new value outside the range would invalidate the calculation). Standard deviation, on the other hand, offers us an insight into how closely data is distributed towards the mean, and gives us some predictive power into expected behavior of new data.

Standard deviation informs us how distance the value is from the sample mean which is basically the expected value, this tells us how different the data is from the expected value. This is more useful than the range as the range does not give us information about the expected value and hence the variability. Standard deviation helps us deduce much is the variability from the expected value.

First of all, I would like to state the definitions of standard deviation and range. A standard deviation is a measure to evaluate the spread of the dataset. It does by calculating the square root of average of square of difference between each value in the dataset to its mean. While range is another measure of variability that provides the spread of the data by measuring the difference between the max value of the dataset and minimum value of the dataset.

With that said, standard deviation is more effective to measure the variability of the dataset since it considers every value in the dataset. That reveals the information density of the dataset. And also standard deviation reveals if the data follows 68-95-99.7 rule.

While range relies on the extreme values of the dataset. One massive outlier may skyrocket the value, if the data is tightly packed.