Find the variance and standard deviation of each set of data to the nearest tenth. 321, 322, 323

Find the variance and standard deviation of each set of data...

Key Concepts

Variance

Variance quantifies how spread out the data points are around the mean by calculating the average of the squared differences between each data point and the mean. This measure of dispersion helps in understanding the overall variability within the dataset.

Mean

The mean is the average of a dataset, determined by summing all data values and dividing by the number of values in the dataset. It provides a central point of reference for the distribution of data and is foundational in calculating further measures of variability.

Standard Deviation

Standard deviation is the square root of the variance, bringing the measure of dispersion back to the same units as the original data. It indicates the typical distance that data points deviate from the mean, making it a useful metric for assessing the spread or consistency of the data.

Transcript

00:01 Okay, so for number four, we need to find the variance and center deviation of the given list.

00:06 And so the list goes from 321 and goes in order up until 330.

00:12 So by counting that out, that is 10 numbers.

00:16 So the first thing we need to do whenever you're finding variance or standard deviation is to find the mean, the x bar.

00:22 So we're going to make sure that whenever we add up all those numbers that we divide by 10 because there's 10 numbers in that list.

00:29 So we're going to go ahead and add up 321 plus 322 plus 323 plus 324 plus 325 plus 326 plus 327 plus 328 plus 329 plus 330 and we get 3255.

00:52 Okay.

00:53 And then when you divide by 10, that's going to get us 325 .5 .5.

01:00 And so we definitely are going to be using that average quite often in step two because the part variance is you're trying to see how far spread out your mean is away from the numbers in the list.

01:13 So i'm going to go ahead and we're going to be taking all the numbers in our list and we do each of them subtracted by the mean.

01:21 So i'm going to be rewriting 325 .5 pretty often here.

01:25 Oops.

01:28 Five cleaned up.

01:40 There we go.

01:43 Sometimes the stylus has its own mind, i swear.

01:47 All right, so 325 .5, 325 .5.

01:54 325 .5.

01:56 And this is a great way to help keep yourself organized the way that this is kind of set up.

02:00 It's a great way to show your work because i imagine that is something you might have to be doing.

02:07 Obviously, if you, are allowed to use technology and you were taught to use the technology methods, then feel free to do that as well, just to be able to check your work.

02:18 Nothing wrong with verifying the right answer.

02:30 Okay.

02:32 All right, so we're going to be subtracting and we're going to be squaring.

02:34 Now, the reason why we square is because sometimes you're going to end up with a negative difference, and we want to always keep variance and snow deviation positive.

02:43 So by squaring it, that will ultimately always fix any negative you might get.

02:48 So i'm going to do 321 minus 325 .5, and i get negative 4 .5.

02:55 We're going to square that, and that's going to get me 20 .25...

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