# Standard Deviation Problems with Solutions

Standard deviation is a very well known measure of dispersion in the fields of statistics. If you are studying the post metric syllabus of the stats then you are most probably going to come across this measure and it will form the significant part of your exams as well.

As, the name suggests standard deviation is basically the measure of the amount of variation or the dispersion in the given set of values. Here we consider the value of mean for the dispersion using the standard deviation measure to figure out the actual amount of variation or the dispersion.

If the actual outcome number remains close to the mean values, then we have the low amount of standard deviation while if the actual outcome numbers remain far from the mean then the amount of standard deviation also increases.

The zero standard deviation indicates that the outcome number is just equal to the mean and you can plot the figure of standard deviation using the normal distribution curve for the better representation of the whole data.

## Standard Deviation with Examples

Well, if you want to have the better understanding of the standard device, then we believe that you must check out the practical example for the working of the standard deviation.

Here for example we have the score of the numbers of the students in the class whose scores mean is 12, while the actual numbers are as 12,8,2,15,23 and now we are required to figure out the standard deviation out of the above mentioned score of the students.

### Standard Deviation Problem Worksheet  As we have mentioned that standard deviation is actually the variation or the dispersion of given data from the mean of such data. Here we see that the actual numbers are slightly/more in the spread out than the mean of such numbers, which is going to raise the bars of the standard deviation.

If the numbers remain close to the mean 12 in the above example then standard deviation would be least spread out, thus with the measure of standard deviation you can actual compare the whole data with the mean and see the amount of dispersion with the standard deviation measure.

Here is the formula of standard deviation by which you can calculate the specific figure of the standard deviation for the given set of values.

Example 1: Example 2: 