Other useful concepts
Example:
To illustrate some other useful statistical measures like standard deviation and range, let us look at the distribution of soldiers' hourly wages in a platoon of 20 soldiers.The table given below shows different wages and the number of soldiers.

Hourly wage in $ Number of soldiers
191
201
214
227
235
242

Let us calculate the variance for these values as explained in the previous section.

The mean for these values = ( 19*1 + 20*1 + 21*4 + 22*7 + 23*5 + 24*2) / 20 = 22
The variance for these value = 0.95 ( Try this problem and confirm the answer)

Variance is one of many possible measures of dispersion, or variation. It is not used very often as a descriptive statistic, because standard deviation is more convenient mathematically. Standard deviation is very closely related to the variance, it is just the square root of the variance. Standard deviation represnted by .

Solution:
The standard deviation for the above problem = sqrt(0.95) = 0.97467
By looking at the table we can tell that there are more soldiers with an hourly wage of $22. This value is called mode. The mode is that value which occurs more often. If there are two, three, or more values that occur the maximum number of times we call that set of data a bimodal, trimodal or multimodal distribution respectively.

Another measure of dispersion is range. Range is the difference between largest and smallest values of the distribution. This measure is useless, if either of the extreme values is infinite.

Solution:

The range of the above soldiers' wages illustration = 24 - 19 = 5

Find standard deviation, range, and mode for the following set of values. 7, 5, 18, 8, 12, 5, 15.