Find the variance and standard deviation of each set of data to the nearest tenth. 48, 36, 40, 2

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

Key Concepts

Variance

Variance is a measure of dispersion that quantifies how far each data point in a distribution is from the mean. It is calculated as the average of the squared differences between each data point and the overall mean, which emphasizes larger deviations and provides insight into the spread of the data.

Standard Deviation

Standard deviation is the square root of the variance, translating the measure of dispersion back into the original units of the data. It represents the average distance of each data point from the mean, offering an intuitive sense of data variability and consistency.

Arithmetic Mean

The arithmetic mean, commonly known as the average, is calculated by summing all the data points and dividing by the number of observations. It serves as the central value of a data set and is fundamental in calculating measures such as variance and standard deviation.

Transcript

00:01 All right.

00:01 So for number three, we are tasked with finding the variance and the standard deviation.

00:09 So the variance is trying to figure out how far away things are spread out from the mean on your list.

00:18 So the first thing we need to do is find the mean in order to be able to find the variance, and then ultimately to be able to find the standard deviation.

00:25 So remember, averages mean you add up all your numbers, and then you divide by however many numbers are in this.

00:30 List.

00:31 So counting out from 48 all the way to the 37, i am counting 10.

00:36 So that is the first thing we're going to be writing down is that we know that we have 10.

00:41 And so then we're going to add up all these numbers.

00:44 So we add up the 48, the 36.

00:48 We're going to add 40, add 29, 45, 51, 38, 47.

00:54 We're going to add 39 and 37.

00:56 And you should be getting 410.

00:59 You should be getting 10.

01:02 You divide 410 divided by 10 and that's going to get me 41 as a mean.

01:07 Now we're going to be using that 41 quite often in step 2.