Question

2. Find the standard deviation of the data set below.
17, 16, 56, 50, 14
Please show me step by step.

Answer 1

First step, find the mean.
You can do that by finding the sum of all the numbers in the data set, then dividing it by the number of elements in your data set.

Answer 2

30.6 ?

Answer 3

@math&ing001

Answer 4

Yep, correct !
Second step is to find the variance.
To do that you take each number in your data set and you subtract the mean from it. Then square each subtraction, and add the squared numbers all together.

Answer 5

Sooo each number subtract that from 30.6 ?

Answer 6

No subtract 30.6 from each number, like x-30.6

Answer 7

Sooo like 17- 30.6? or really x-30.6
Sorry im horrible at math.

Answer 8

Yep exactly like 17-30.6
x is just a random variable.

Answer 9

okay ill do that right now

Answer 10

okay i did that, now how do i do the last part?

Answer 11

Then square each subtraction, and add the squared numbers all together.

Answer 12

The 5 subtractions you got, you square them. Then you add all those squares. After that, divide the sum by (n-1). That's your variance.

Answer 13

ok i understand all of that besides how to square them..

Answer 14

Oh, to square a number is to put it to the power of 2.

Answer 15

okay so -13.6 x 2 ?

Answer 16

Not quite, it's looks like this \(\huge{x^2}\)

Answer 17

right, im just having trouble with all of that now, im pretty confused

Answer 18

It's totally ok.
So in the first example it would be (-13.6)²=184.96

Answer 19

ok so, (-14.6)2 = -29.2 ?

Answer 20

if thats correct, do that to all of them?

Answer 21

did that wrong, i fixed it

Answer 22

213.16 ?

Answer 23

Cool !

Answer 24

is the 213.16 correct

Answer 25

Yep, correct !

Answer 26

ok, finished alll of that, now i do what

Answer 27

You added them and divided by (n-1) too ?

Answer 28

not yet

Answer 29

OK when you do tell me what you get =)

Answer 30

i got 1695.2 when adding

Answer 31

Didn't check but it seems right.

Answer 32

okay then divide that by one ?

Answer 33

You divide by (n-1), n being the number of elements in your data set

Answer 34

1695.2/1 ? now thats where im going to be confused

Answer 35

ohh okay never mind

Answer 36

(5-1) ?

Answer 37

Yep !

Answer 38

so i got 4 ? when it comes to (5-1) then what lol

Answer 39

So you divide what you got (1695.2) by 4 =)

Answer 40

I got 423.8

Answer 41

Yep that would be your variance.
Finally you find the square root of the variance, and you have your standard deviation.

Answer 42

Okay how does that work.. lol

Answer 43

Standard deviation is \[\sqrt{variance} = \sqrt{423.8}\]

Answer 44

ok, whats that or what do i do from here

Answer 45

Just evaluate the square root to get your answer.

Answer 46

okay and thats all ? .-.

Answer 47

Yep !

Answer 48

these math terms got me so confused lol thank you so much! ill try figure the last part out

Answer 49

You're not supposed to do it by hand just use a calculator :P
\(\sqrt{423.8}=20.6\)
You're much welcome !

Answer 50

You just saved my life !!!!! Thank you!!!! :D

Answer 51

^^