All language subtitles for 05 - Analyze a population using data samples

- [Instructor] When you gather data about your business,

you will often analyze samples

instead of an entire data set.

And that's because gathering data can be very expensive

both in terms of money and time.

That said, you should gather as large a sample as you can,

interview as many customers, review as many products,

to make sure that you have all the data that you need.

More is better.

From there, you can estimate the data population's

standard deviation based on that sample.

And then you determine your desired confidence level.

Do you want to be 90% confident in your result?

Do you want to be 95% confident, 98, 99?

It all depends on how precise you want to be.

From there, you can calculate your margin of error

and that will tell you, at your given confidence level,

how much above or below your values will be.

So what is margin of error?

Well, let's say that each bottle contains 12 ounces

of olive oil with a margin of error of plus or minus

0.3 ounces at a 95% level of confidence.

So you want to be 95% confident that the true margin

of error is plus or minus 0.3 ounces

based on the mean of 12.

You rarely see the confidence level stated explicitly

in political polls or in business analysis

but it is always there and it is useful information.

You calculate the margin of error,

first by calculating your standard error.

And that is the standard deviation of the data set,

in this case the sample that you've taken,

and dividing that by the square root

of the number of measurements.

Margin of error is then standard error times your Z-score.

And the Z-score is the number of standard deviations

that your confidence level is from the mean.

A Z-score of one includes about 68% of values.

But being 68% certain about something is not reliable.

I recommend going for higher values.

And I have those listed in the chart on this slide.

Here we have some of the commonly used Z-scores.

And you can see the confidence level and the Z-score

that is associated with them.

Most analysis in business operates at the 90%

or 95% confidence levels so Z-scores of 1.645

and 1.96 respectively.

Getting enough samples to reach the 98%

and 99% confidence levels can be expensive.

If you can do it, great, but 90 and 95%

are much more common.

With all this in mind, let's switch over to Excel

and calculate the margin of error for a data sample.

I've switched over to Excel and my sample work

because 01_05, Margin of Error.

And you can find it in the chapter one folder

of the exercise files collection.

And I have set up the problem that I described earlier.

So in cell B3, you see that we have

a standard deviation of 0.1.

And again, this is the standard deviation of olive oil

put into bottles at a factory.

So we have a standard deviation of 0.1,

a certainty level of 95%.

And then we can put in the Z-score for 95%.

I have those listed over here on the right.

So I see that 95% is 1.96.

So I'll click back in cell B5, 1.96.

I could create a formula to do a look up

but I don't think that's necessary here.

And finally, we have our number of measurements.

For the standard error, I need to divide

the standard deviation by the square root

of the number of measurements.

So in B8 I'll type equal.

And our standard deviation is in B3.

And I will divide that by the square root,

and that function is SQRT, of the number of measurements,

which is in B6.

Right parentheses and Enter. And I get 0.016.

Okay, now I can look at the margin of error.

And that, as the formula on the right reminds us,

is the Z-score, which is in B5,

multiplied by the standard error in B8 and Enter.

And we have a margin of error of 0.031, which is rounded

to two digits, the 0.03 that we saw earlier in the movie.