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

Let's now consider linear regressions of standard scores.

Standard deviation of the distribution

And if we want to take it to the next level and figure out the standard deviation, the standard deviation is just the square root of the variance, which is equal to the square root of p times 1 minus p.

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

Standard deviation for the total population

Sample standard deviation

As we know, this gives us an estimated mean.

Standard deviation of the standard logarithmic distribution

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.

And then these two lines I drew right here, these are 1 standard deviation below and 1 standard deviation above the mean.

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.

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.

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

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

So, we have the some of the squares and we have the cross products.

And finally, this is the inverse of the standard score z that I've told you.

But after we take the square root, it only gets bigger by 1.5 since the square root of 1.5 squared is equal to 1.5.

It looks like it's like 80 something percent, maybe 90 percent roughly.

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

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

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 I want to get into your brains is not the complexity of the formula. I want you to really understand how this formula is constructed.

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

This is the standard deviation.

And it's real easy to convert a raw score to a Z score, you just use this formula.

So it's kind of, not exactly, but kind of the average distance from the mean.

What's the probability of tails, and if tails actually occurs, the outcome is 0.

Let's practice this. I'll give you a couple of quizzes now.

As I said the work is done for us.

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

Expressed through standard deviation Values given over accidental errors.

There's variance in the sample SD squared.

If we were to do this 1000 for a fair coin, you expect the outcome of the mean to be 0.5.

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