Find the variance and standard deviation of each set of data to the nearest tenth. 2.4, 5.6, 1.9

step 1 that will always be your first step. So you look at your list and you count how much you have in

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

Key Concepts

Variance

Variance is a measure of dispersion that quantifies the average squared deviation of each data point from the mean. It gives insight into the spread of the data by reflecting how far the data points are distributed around the mean. A larger variance indicates that the data points are more spread out.

Data Set

A data set is a collection of numbers or values that are analyzed statistically. It forms the foundation of many statistical analyses, where each individual number represents an observation from a process or experiment. Understanding the concept of a data set is crucial as it is the starting point for calculating various statistics like the mean, variance, and standard deviation.

Mean

The mean, or average, is a measure of central tendency that represents the sum of all data values divided by the number of values. It provides a single value that is typically representative of the entire data set and is used as a reference point when determining how data points deviate from this central value.

Standard Deviation

Standard deviation is the square root of the variance and provides a measure of spread in the same units as the original data. It is used to understand how tightly the data points cluster around the mean. A smaller standard deviation indicates that data points are closely grouped around the mean, while a larger standard deviation shows greater dispersion.

Transcript

00:01 That will always be your first step.

00:01 So you look at your list and you count how much you have in your list.

00:04 It turns out there's nine.

00:06 So remember, the mean or the average is the same as adding up all of your numbers in your list and then dividing by nine.

00:14 So we're going to add up the 2 .4 plus the 5 .6 plus the 1 .9 plus the 7 .1 plus the 4 .3 plus the 2 .7, and 4 .6 and the 1 .8 and the 2 .4 and you get 32 .8.

00:38 All righty.

00:39 And then you divide that by 9 and you get 3 .6 officially rounds to the nearest 10th of 3 .6.

00:46 So you're going to be using that 3 .6 quite often in step 2.

00:51 So variance is seeing how far away your spread is from the mean.

00:55 So we're going to take all the numbers in the list.

00:58 All nine of them and subtract the 6, the 3 .6.

01:03 So i'm going to write 2 .4 minus 3 .6 and 5 .6 minus 3 .6.

01:09 And notice we're squaring because when you subtract, sometimes you're going to end up with negatives, but we can't have negatives when we're doing variance or standard deviation.

01:22 So we square that.

01:23 And remember whenever you square a negative, it becomes positive.

01:26 So that's why the squaring is going to happen eventually.

01:31 So we're going to subtract first, then square for all nine of these items in the list.

01:36 So 2 .4 minus 3 .6, and then we square it.

01:42 We get 1 .44.

01:46 Okay.

01:47 5 .6 minus 3 .6.

01:51 And then we square it, we get 4.

01:56 1 .9 minus 3 .6...