We have 10,000 people who received Treatment A. Their average loss is 10 pounds.

A common measure of intelligence, IQ, is distributed with a mean of 100 and a standard deviation of 15.

Std. deviation

Std dev.

Deviation

Std. dev

Standard deviation

standardDeviation

Standard Deviation

If there's one thing you want to take home from this class that is that as you get more data as a statistician, your confidence increases so your confidence interval shrinks, whereas of course more data doesn't change the standard deviation.

We also applied it to 10,000 people. Our average loss in this case was 20 pounds.

It just moved over to the right by 5. If I were to try to make the standard deviation smaller we'll see that the whole thing just gets a little bit tighter.

What are the mean and standard deviation of this distribution of the distance between the initial position and the final position?

That is to say, If I were to look at the salaries, there is a well defined mean of course.

It is equal to the square root of the sum of the deviations in the y's over the deviations of the x's.

Let's now consider linear regressions of standard scores.

Standard deviation of the distribution

That means the standard score shrinks.

We said it's 1, and so because it's not 1 it must be less than that.

Sample standard deviation

Can you guess what the effect is of adding 1000 to your salary on the mean and the standard deviation?

To see this, recall that as you just discovered b is equal to r times times the standard deviation of y over the standard deviation of x.

13.5 is the data point, 7.5 is the mean. Their difference is 6.

Don't discuss this in the forums. That's kind of secret, but what does this mean?

STD is the standard deviation of the distribution.

Standard deviation of the normal distribution

This is just simple algebra. So here's the formulas for Z, that's from

And I'll just call this, what's the probability that I land between 1 standard deviation the mean is minus 5 one standard deviation below the mean is minus 15 and one standard deviation above the mean is 10 plus minus 5 is 5.

What is it? If you don't mind.

And sometimes it's easier to think in terms of sigma.

See, I'd been guilty all this time of what's termed 'speciesism'.

Standard deviation for the total population

We add those up we get 250 and now we divide by 5 to get back our 50.

More or less?

Can you tell me what is the mean mu of the Ys, what is their standard deviation sigma what is their variance sigma squared and what is the value of this point now Yi and what is the standard score z of Yi.

Since Yi is just the individual observation Xi multiplied by 1.5, it's 1.5 times 9, which is 13.5.

Standard deviation of the standard logarithmic distribution

As we know, this gives us an estimated mean.

Suppose now, I give everyone a raise of say 10,000, what do think is the new mean and the new standard deviation following µ' and σ' can you answer these questions?

Gaussian, so this can have a different mean and a different standard deviation than the other features, and so on, up to XN.

And the correct answer is smaller.

What do you think is the new mean and what's the new standard deviation important?

And now we get to the confidence interval.

The mean is 4, and the variance and the standard deviation are 0.

And the way we estimate that is to rely on the principles, of the central limit theorem, and calculate standard error, by looking at the standard deviation, in our sample, and the size, of our sample.