Calculate the range population variance and population...

Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 6,7,8,9,10,11,12,13,14,15 Range: Population Variance: Population Standard Deviation

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 Find the range variance in the standard deviation of this list of numbers.

00:05 I already have them listed in order here, so let's start with our range.

00:09 Our range is going to be the largest, minus the smallest, which is going to be a range of nine.

00:14 Now to get the variance in the standard deviation, we're going to need to find the mean.

00:20 And to find the mean, we're going to add each one of these together and divide by the number of numbers, which in this case is 10, and that's going to be our value of n.

00:29 So i'm going to have 105.

00:33 Let me double check that real quick.

00:39 That's correct.

00:41 Divided by 10.

00:43 So my main x bar is going to be 10 .5.

00:48 Now to get our variance, we need to find out how far each one of our values is from the mean.

00:54 So we're going to subtract them.

00:56 Now, we don't have to worry about the positives or negatives because we're going to end up squaring it.

01:00 So i'm going to take 10 .5 minus 6, 7, 8, 9, 10, et cetera.

01:05 So that's going to be 10 .5 from 6.

01:07 That's going to be 4 .5.

01:10 This is going to be 3 .5, 2 .5, 1 .5, 1 .5, 0 .5, 0 .5, and that's going to be another 1 .5, 2 .5, 3 .5, and 4 .5 .5.