What is the standard deviation? How do I figure it out

Question

50,51,53,54,55,55,57,57,59,62,62,63,63,65,66

Answer 1

Hi Wendy from Morrisville, VT. Hope you had a great day off from school.
I am here to help, however, I will not give you the answer. I will help you understand to learn how to solve these kind of problems so you will know how to solve them.

So, to  begin with, you will start with putting all the values in this set in a progressive order. In the set you have provided, it is already done for you. If you have another set, you have to start with writing the set of numbers in a progressive order.

Then next step is to determine the number of values which are in the set. In this case, you will count there are 15 values in this set of numbers, correct? 

Step number 2 is to add up ALL the value to get the total:

50 + 51 + 53 + ......+ 66 = the sum of all the values. I will let you do this part.

Step number 3 is to find the mean, the average of the set of numbers. Do you know how to do this? Hint: it is the quotient of the sum and the number of values in the set. This means what?

       Sum of the values of the set divided by number of values = the mean

                 Sum of the values ÷ 15 = the mean or the average of the set

 Let's say your mean, the quotient is 57, the answer you got after adding up all the values and dividing it by 15. 57 is the average or mean.

Now, step number 4, subtract each of the values in the set from the mean that you calculated. Like this:

        50 - 57  =  -7

        51 - 57  =  -6

        53 - 57  =  -4

       ..........

        66 - 57  =  11

After you subtracted each of the values, (remember there should be 15 values) add all of those values for another sum. Here is an example:

     -7 + -6  + -5...+ 11  =  some value, the sum of your calculation.

The last step is to divide the sum you just calculated, it might be a negative number, it might not be, by 15 (which is the number of values you added together)

This last value is your Standard deviation, written like ±4...this is just an example. You will say the Standard deviation of the set of number

    {50,51,53,54,55,55,57,57,59,62,62,63,63,65,66} is ±4

Let me know if you have any further questions. 

Jon