Question

How do I find standard deviation, and mean.

Im working out of a summer work book there is about 100 of these questions. Could you help me do a few so I get the Idea?

Heres the exact question:
Find the mean and standard deviation of each data set. Round to the nearest hundredth.

1.4,8,5,12,3,9,5,2
2.102,98,103,86,101,110
3. 8.2,11.6,8.7,10.6,9.4,10.1,9.3

Answer 1

Sure. The mean is what we normally think of as the average.
It's the sum of all the values divided by the number of values

Answer 2

Let's do it for the first set of numbers. But first, is that a 1.4 or a 1,4, ?

Answer 3

On the first one?

Answer 4

Yep

Answer 5

Its problem #1, so the first number is just 4

Answer 6

Ah, of course.

Answer 7

OK, so add all the numbers for problem 1.

Answer 8

48?

Answer 9

And how many are there?

Answer 10

There is 8 numbers

Answer 11

So the mean is the total divided by n

Answer 12

so 6?

Answer 13

Yes.

Answer 14

So thats how I find the mean? How do I do standard deviation?

Answer 15

Now the next step is a little tedious. We need to subtract each value from the mean

Answer 16

We had 4,8,5,12,3,9,5,2
So I get -2, 2, -1, 6, -3, 3, 1, 4 Does that sound good?

Answer 17

Wait how did you get that?
so we take 4 and subtract that from 6? and then the next number and so on?

Answer 18

Yes

Answer 19

Subtract 6 from that

Answer 20

oh ok got it.

Answer 21

I said it wrong

Answer 22

It ok I got so from there what do we do with -2,2,-1,6,-3,3,1,4

Answer 23

Subtract the mean from each number. Now, the next step is to square each of these differences:

-2, 2, -1, 6, -3, 3, 1, 4
4, 4, 1, 36, 9, 9, 1, 16

OK?

Answer 24

Then find the sum of that

Answer 25

What do you get for that?

Answer 26

Wait so I sqaure the bottum rowe?

Answer 27

row

Answer 28

No, the bottom row is the square of the row above, I already did that.

Answer 29

Ohh ok got it. So i sqaure what I got from subrtacting the mean.

Answer 30

Yep, and the answer I get is 80. Check?

Answer 31

Yes I got 80

Answer 32

Two more steps.
What we did so far is to calculate the mean, find the differences from the mean, square them, and add them all up. Next step is to divide by n (which is 8, here). That gives 10. This is the called the variance of this data.

Answer 33

How did you get 8?

Answer 34

There are 8 numbers in the data set.

Answer 35

Ohh ok got it, so from there we now have 10?

Answer 36

Yep. Before we do the last step I should warn you that sometimes they want you to divide by (n-1) rather than n. But that's really too advanced to worry about here. Just be sure to check your lecture notes or whatever to be sure what they want for this step. OK?

Answer 37

ok got it

Answer 38

Last step is to take the square root. The standard deviation is the square root of the variance.

Answer 39

3.16?

Answer 40

Yes!

Answer 41

ohhh ok got it! Thats actually not that hard. Hhaha thank you soo much for breaking it down!!!

Answer 42

These are very tedious to do by hand so I don't envy you doing 100 problems. Can I just point out one interesting thing? The squaring of differences has the result that numbers that are farther away from the mean count a lot more toward the standard deviation.

Answer 43

Good luck.

Answer 44

Its a work book! Haha i didnt plan on doing all of them. But thank you soo much:)))