Variance and Standard Deviation using HP 10BII Calculator

All right welcome back. This is the second portion of our video series of the using to calculate statistics using the HP 10 B 2 or 10 B 2 plus calculator and this go-around. Okay, we're going to discuss calculate the variance and standard deviation with these are points.

I'm gonna do is. Okay, well let go we did the mean.

You can't calculate variance without the mean.

Now that we have the mean there's a quick way of doing it using your calculator you already have your data points Roary know what the mean is right.

Like from the last video I showed you guys how they get the mean.

You could say it's orange key you hit the 7 key on your calculator and it gives you the mean.

We have the mean here.

What we have to do now is get the variance and the variance is uh it's pretty simple.

To get the variance first let me hit clear clear that out the formula if you want to keep up and the follow you go to page 142 in the book statistics for managers using Microsoft Excel seventh edition by David Levine David Steven and Katherine zaga back and that's the seventh edition of it it's the global edition.

And I'm when what I'm doing is I'm going over standard deviation on page 142 using the same data of the time and a data that we use in the last video to calculate statistical mean.

Standard deviation I mean the variance is you have to calculate variance in order to get the standard deviation.

Once you have the variance the variance is the standard deviation is just the square root of the variance like I said we're going to do standard deviation let me show you how to do that and then I'm going to show you how to reverse it.

You can get the variance because I'm giving these scenarios for base for people especially who has to learn how to use a calculator for examination purposes.

If you look at page 142 you'll see you'll see the formula is s squared equals you know the s squared equals the sum of X the variable of X minus the mean squared divided by the number of data points minus 1.

The quick way to calculate that I'm going to show you here you see the 8 key right here you can see the 8 key that s right here is means the standard deviation of X. All right.

If you want to get for these data points it's already still in memory.

We know it's still remember if you just want to check if still remember you can see how many data points do I have in there if the blue key they hit the N and tells you that. This is 10 data points as you see it state staying one to ten and that represents the data points right so. Okay, now that we got that it's hit the Clear button. Okay.

We're gonna clear that out and how you get to standard the standard deviation of those data points you see this S right here over the eight.

We're going to hit that you're gonna hit send the deviation gives me the standard deviation right.

The variance if you want to get the variance and it's kind of backwards and they used you guys are used to doing getting the variance first and then you do the square root of the variance in order to get it to get the standard deviation but we're gonna we're gonna do it I'm going to show you a faster way of doing it because actually on the calculator it doesn't there's no calculation for variance right on the calculator whether there is a calculation for standard deviation which if you know if you square the standard deviation it will give you the variance because the variance is what it's the square root of the variance.

If you square this.

Here's the square key right here as you can see the plus key on your calculator you see x squared.

That's your square root.

You take that amount that's with standard deviation you hit the get the orange key and then you hit the plus key to square it.

That's gonna be your variance calculation and you're probably saying well how did you figure that out how did you figure out if that's correct.

What I want to do is if you go to page 144 and in the statistics books the statistics for managers using Microsoft Excel for the page 144 you can see table 3.1.

If you look at down below the table you can see the calculations and you're gonna see that's the variance that I calculated you see it comes up to 45 point 82.

It was pretty neat right.

How to do it faster but if you want to check and make sure the variance is correct you could reverse-engineer this right and when I mean by reverse engineer this. Okay, you got the variance.

What is the variance right.

We know that the formula as you can see on page 144 it's the sum of its the sum squared of all the data points - the it's ten the ten minus one meaning the number of data points.

In order to do that.

I would multiply this number by 9 right.

If I take that number and I say multiply by 9 it's gonna give me as you see on page on page 144 you can see it gives me a a it's it's correct it's it's four hundred and twelve point four which I have here for twelve point four.

If you take this before I multiplied it by nine now I'm going to divide it by nothing.

To make sure that you see that it I'm correct.

If you take that for twelve then you had divided by nine and equals forty five point eight two which is your variance.

Now you have the variance then you do what do what you square root it till you hit the orange key it's square root and then that's your standard deviation and that's it.

In my next video let me show you how to calculate the coefficient variation for the same data set you.

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