### Basic variation in statistics range standard deviation and Variance

Range;- The range is one way to measure the spread of a set of data. It is defined as the difference between the highest value and the lowest value in a data set. The range is always positive. The larger the range the greater the spread of the data. The smallest range you can have is zero.

This would indicate that every value in the data set is the same. The range can sometimes be misleading and may not be the best measure of variation in a data set. For example: Suppose 2 Statistics classes take a quiz.

The first class has the following results 2, 10, 10, 10, 10, 9, 10, 9, 10, 10. The range of this set of data is 8 (10-2). The second class has the following results, 10, 2, 3, 5, 6, 3, 4, 5, 2, 6. The range of this set of data is the same 8 (10-2). However, the second set of data is more spread apart than the first set of data. The range does not indicate this, it is simply a measurement of the difference between the largest value and the smallest value. We need some other measurements to tell us more about the spread of the data.

Standard Deviation; -- Another measure of the spread of data is known as the standard deviation of the data. The standard deviation takes into consideration not only how spread out the data is, like the range, but how far each data point falls from the mean. A nice way to remember the standard deviation is that it is the average distance a data point falls from the mean. Once again the larger the standard deviation the further spread apart the data will be. You will be asked to calculate the standard deviation by hand once or twice. After that you may use the calculator. See the attached document for the formula to use for standard deviation. It is important that you understand how the standard deviation is calculated. It will give you a better sense of its meaning with regard to the data.

Note that the standard deviation is the square root of variance, and so the formulas of calculating both measures are not different at all.