We will begin by finding the advantages of using the range to describe a data set. Then we will analyze why the standard deviation is a more reliable measure than the range.
Advantages of Range
Recall that the range is the difference between the maximum and minimum value of the data set.
Range=Maximum - Minimum
One advantage of using the range to describe the variation of a set of data is that finding the range is straightforward. Complex calculations are not needed in order to find it. Additionally, when we only want a quick idea of the distribution of our data, the range is the fastest method to use.
Standard Deviation vs Range
The standard deviation of a data set measures how much a typical value in the data set differs from the mean. Recall the formula for the standard deviation of a data set.
σ=sqrt((x_1-x)^2+(x_2-x)^2+...+(x_n-x)^2/n)
In this formula, n is the number of data values in the data set and x_1, x_2,..., x_n are the data values. With this, let's state some facts about standard deviation.
The standard deviation uses all the data values, while the range only uses two.
With standard deviation, we can look at any single piece of data and see where it falls in relationship with the mean.
It provides more information overall for each piece of data.
Because of this, standard deviation is a more reliable measure of variation than the range.
