Question

I NEED HELP NOW!!!!!!!
What is the variance of the following data? If necessary, round your answer to two decimal places.
82, 44, 67, 52, 120
Please can someone just give me the answer?

Answer 1

Well, to solve this problem, you need to know what 'variance' mean.
A variance is defined as, "The average of the squared differences from the Mean."

So find the mean of "82, 44, 67, 52, 120"
Do you know how to find the mean of the following data set?

Answer 2

Yes I do

Answer 3

Alright. Then what is mean of the data set?

Answer 4

hmm...I think it's 164? I'm not sure sorry.

Answer 5

To find the mean you add up all of the data in the data set, then divide it by the total amount of data in the data step.

So what is the sum of 82, 44, 67, 52, 120?

Answer 6

Oh! I thought you took the biggest and smallest number and added them up....but I think that's with range isn't it?

Answer 7

The range is the biggest value subtracted by the smallest value.

Answer 8

So what is the sum of 82, 44, 67, 52, 120?

Answer 9

Oh okay that makes more sense. The sum is 73

Answer 10

Oh really? What is 82 + 44?

Answer 11

Oh. Wait. The mean is 73*

Answer 12

Okay. So the mean is 73. What do you do next?
Well, you want to subtract each data from the data set by the mean, 73.

So what is:
82 - 73 =
44 - 73 =
67 - 73 =
52 - 73 =
120 - 73 =

Answer 13

9
-29
-6
-21
47

Answer 14

Oh my bad. Didn't see that.

Answer 15

Now square: 9 -29 -6 -21 47

Answer 16

Then divide it by 5 to get your variance.
I know, too much steps.

Answer 17

Now, now. Why take so much pain when you know the definition of Variance? It's mean of squares - square of means.\[ \frac{ [82^2 + 44^2 + 67^2 + 52^2 + 120^2 ] }{ 5 } = 6050.6\]
Now, mean is 73. And \[73^{2} = 5329\]
So, variance is 6050.6 - 5329 = 721.6

Answer 18

No. It is not 721.6.

Answer 19

Oh yeah, make sure you absolute value it after squaring it.

Answer 20

Example, after squaring -5, you get -25. Correct? When you absolute value it, you get 25. So if you get any negative number after squaring it, get rid of the negative sign.

Answer 21

Variance can never be negative. I am sure of what I have done, but if there are any calculation errors, please check. But I have used the computer calculator and I wish there isn't any error.

Answer 22

And, after squaring -5, you will never get -25. You will get only 25.

Answer 23

No. After squaring -5, you get a negative 25.

Answer 24

Sorry, for being rude, but please go and open a mathematics book before continuing any argument on this.

Answer 25

Alright. My apology.