Question

What is the standard deviation of the following data? If necessary, round your answer to two decimal places.

12, 13, 8, 13, 9, 11, 12, 9, 1

Answer 1

I don't think @heretohelpalways that we want the mean absolute deviation for this problem. We need the standard deviation.

Answer 2

The steps to do this are:
1. Find the mean of the data. (Find the average)
2. Then find subtract each data point from the mean and square the result.
3. Find the mean of the "square differences" we found in step 2.
4. Take the square root of Step 3 and we are done.

This is easier to see in a table. Which I will show below.

Answer 3

Here's the start of my table.

Answer 4

Let's go ahead and do step 1. What is the mean of the data? To do this, just add up all the data and divided my how many we have.

Answer 5

9.8?

Answer 6

12 + 13 + 8 + 13 + 9 + 11 + 12 + 9 + 1 = 88

Then, divide this by 9 (that's how many we have), this gives us 88/9 = 9.8.

You beat me! Good! :D

Answer 7

Now, for the annoying part... we have to subtract the mean from each of our data points. So, for example, we do 12 - 9.8 = 2.2. Then we repeat this for all the other points... BORING! But, not that hard. :)

Answer 8

When you are done, you will get something like this (I'm cheating since I have a computer that does this for me...)

Answer 9

Does that make sense so far?

Answer 10

Yep! got it so far, thanks

Answer 11

Great! Now, for the second part of Step 2. We need to "square" (multiply the number by itself) each of the differences we just found. What am I trying to say? For example,

The first difference was 2.2. So find 2.2^2 = 2.2 * 2.2 = 4.84.
And do this for each of the differences... BORING AGAIN! But not hard.

Answer 12

You should get something that looks like this

Answer 13

Phew! Almost done! Now, we find the mean (average) of these crazy squared numbers. Add them up, divide by how many (9) and we get: 12.6 about.

Answer 14

This number we just found is called the "variance" of the data. The standard deviation is the square root of this number. So just find sqrt(12.6) = 3.6 and we are done.

Answer 15

Got it! Thank you so much, that was very well explained!

Answer 16

Glad to help! No point to make it harder than it already is! :) Good luck!