Find the variance and standard deviation of each set of data to the nearest tenth. 43, 56, 78, 8

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

Key Concepts

Arithmetic Mean

The arithmetic mean is the sum of all data values divided by the number of values. It provides a central value around which the data points are distributed and is essential when calculating variance and standard deviation.

Variance

Variance is a statistical measure that quantifies the average squared deviations from the mean. It provides insight into how spread out the data values are around the mean, and a larger variance indicates more diversity in the data points.

Standard Deviation

Standard deviation is the square root of the variance and measures the average distance of data points from the mean in the original units of the data. It is a key indicator of data dispersion and is useful in comparing variability across different datasets.

Transcript

00:01 Alright, so for number five, we need to find the variance, the standard deviation.

00:06 But before we do that, we have to find the mean of all of these numbers in the given list.

00:11 So this list is pretty large.

00:13 Turns out there are 17 numbers in this list.

00:17 So what you're going to have to do then is add up all those numbers and then divide by 17.

00:22 So we're going to do that first.

00:24 So we're going to have 43 plus 56 plus 78 plus 81 plus 1.

00:31 47 plus 42 plus 34 plus 22 plus 78 plus 98 plus 38 plus 46 plus 54 plus 67 plus 58 plus 92 and plus 55 all together it gets us 989 so we're going to write down 989 here and we're going to divide it by 17 and we're going to get a decimal that we're going to have to round so we're going to round the nearest tenth, so you should get 58 .2 approximately.

01:11 Now this 58 .2, this mean is very important because that's how we can measure the spread or the variance from the mean.

01:19 So we're going to use the mean and basically use all of these numbers in this list and subtract this number from the mean with the mean, and then we've got to square it.

01:29 Now the reason why we square everything is because we want to keep things positive.

01:34 So again, our mean is 58 .2, and we're going to reuse this number several times in this list.

01:41 So 58 .2, 50, that's a point there, 58 .2, 58 .2, 58.

01:56 So on.

01:58 Yeah.

01:59 The mean is very important.

02:00 It gets used quite often in these problems.

02:21 Okay.

02:22 Almost there.

02:29 And this is one of the longer ones because the list is so long, it's going to have this long of a list.

02:34 And if you have access to doing something with technology, like to be able to find this with technology and your teacher allows that, that's 100 % okay.

02:42 But this is just how you show your work if you are required to.

02:48 All right, so we're going to subtract and square.

02:51 So we're going to go ahead and go through the list and do that.

02:53 So if you're already 3 -98 .2 gets me a negative, but remember when you square a negative, you get a positive.

02:59 So you should get 231 .04 for that first one.

03:08 56 minus 58 .2 squared gets us 4 .84.

03:21 0.

03:23 78 minus 58 .2 squared.

03:30 392 .04.

03:38 81 minus 58 .2 .2 squared.

03:45 19 .84, 47 minus 58 .2 squared gets us 125 .44.

04:07 42 minus 58 .2 squared gets us 262 .44.