The given values represent data for a population. Find the variance and the standard deviation f

The given values represent data for a population. Find the...

Key Concepts

Population

In statistics, a population refers to the complete set of items or individuals that are the subject of a study. Population data is used when the analysis involves every member of the group, which affects how measures of dispersion like variance and standard deviation are calculated compared to sample data.

Mean

The mean is the arithmetic average of a set of numbers and serves as a measure of central tendency. It is calculated by summing all the values in the dataset and then dividing by the number of values. The mean is a crucial component in calculating variance and standard deviation as it represents the central point around which individual data points are measured.

Variance

Variance is a measure of dispersion that quantifies how much the data points in a dataset deviate from the mean. For population data, it is calculated by taking the sum of squared differences between each value and the mean, and then dividing by the total number of data points. This measure provides insight into the spread and variability of the data.

Standard Deviation

Standard deviation is a commonly used measure of dispersion that represents the average distance of each data point from the mean. It is derived by taking the square root of the variance. This measure is intuitive as it shares the same units as the original data, making it easier to interpret in practical terms.

Transcript

00:01 Okay, so the question here is to find the variance and standard deviation of this set of data right here.

00:13 And we're given that it is a population, not a sample.

00:18 So because these numbers are a bit hard to work with, and it would be too time -consuming to go through the entire process on my part of finding the entire mean.

00:30 Finding the mean, then taking each and every difference to the mean, especially since we find out later that the mean isn't even a whole number, then we take the square of the differences, sum them up, etc.

00:42 I went ahead and actually used an online calculator.

00:45 I apologize for cheating a little bit, but it would just be way too time consuming on my part.

00:53 But i can go ahead and describe what this calculator is doing.

00:55 I think it's best if i'd go ahead and describe what this calculator is doing, and maybe do like a few, take a few of each just to show you like if you have to do it manually, then like this is how to do it.

01:08 Okay, so here goes.

01:10 So what i did was i entered the numbers into the text box, marked numbers, as seen here.

01:15 And what this calculator does, it counts the number of numbers.

01:18 So in this case, there are 15 numbers.

01:21 It sums them up.

01:22 So basically the sum of all 15 of these numbers is 147 and takes the mean, which is a hundred, 47 divided by 15, so we get this 9 .8 right here.

01:33 So now, in order to keep up with the formula, we take the difference of each number and the mean.

01:41 So, for instance, this first number, you can see this 1 .2 right here is just our first number 11 minus the mean.

01:52 And similarly, you see this negative 3 .8 right after the 1 .2 is just our second number 6 minus our mean.

02:01 So, oops.

02:06 So, yeah, that's how the calculator is getting the numbers in this text box right here.

02:12 And it's doing it for all 15 numbers...

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