Name: 統計數據。標準差 (Statistics: Standard Deviation)
Uploaded: 2021-01-14T04:47:21.000Z
Duration: 13 min 7 s
Description: 【看影片學英語】數萬部 YouTube 影片，搭配英漢字典即點即查，輕鬆掌握單字發音與用法，長久累積看電影不必再看字幕。

Let's review a little bit of everything we learned so far

情態副詞

and hopefully it'll make everything fit together

Then we'll do a bunch of calculations with real numbers

and I think it'll really hit the point home.

So, first of all if we're dealing with a-- let me

actually write down, let me make some columns.

So if we're dealing with-- let's see, we could call it the

concept and then we'll call it whether we're dealing with

So the first statistical concept we came up with was the

notion of the mean or the central tendency and we learned

of that was one way to measure the average or central

The other ways were the median and the mode.

But the mean tends to show up a lot more, especially when we

start talking about variances and, as we'll do in this video,

But the mean of a population we learned-- we use the greek

letter Mu-- is equal to the sum of each of the data points

So you're going to sum up each of those data points.

You're going to start with the first one and you're going

We're assuming that there are n data points in the population.

And then you divide by the total number that you have.

And this is like the average that you're used to taking

before you learned any of the statistics stuff.

You add up all the data points and you divide by

We just use a slightly different terminology.

The mean of a sample-- and I'll do it in a different

color-- just write it as x with a line on top.

And that's equal to the sum of all the data

But we're serving the sample is something

And then you go to the lower case n where we assume that

If this was the same thing then we're actually taking the

average or we're taking the mean of the entire population.

And then you divide by the number of data

Then we said OK, how far-- this give us the central tendency.

It's one measure of the central tendency.

But what if we wanted to know how good of an indicator this

Or, on average, how far are the data points from this mean?

And that's where we came up with the concept of variance.

And I'll arbitrarily switch colors again.

And in a population the variable or the notation for

And that is equal to-- you take each of the data points.

You find the difference between that and the mean that

You square it so you get the squared difference.

And then you essentially take the average of all of these.

You take the average of all of these squared distances.

So that's-- so you take the sum from i is equal to 1 to

And then the variance of a sample mean-- and this was a

little bit more interesting and we talked a little bit

You actually want to provide a-- you want to estimate the

variance of the population when you're taking the

And in order to provide an unbiased estimate you do

something very similar to here but you end up

So the variance of a population-- I'm sorry, the

variance of a sample or samples variance or unbiased sample

variance if that's why we're going to divide by n minus 1.

What you do is you take the difference between each of the

data points in the sample minus the sample mean.

We assume that we don't know the population mean.

If we knew the population mean we actually wouldn't have to do

the unbiased thing they were going to do here in

But when you have a sample the only way to kind of figure out

the population mean is to estimate it with sample mean.

So we assume that we only have the sample mean.

And you're going to square those and then you're going to

sum them up from i is equal to 1 to i is equal to n because

And if you want an unbiased estimator you divide

And we talked a little bit before why you want this to be