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.

It should also produce descriptive statistics that look like this. Again, these are from

There's variance in the sample SD squared.

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

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

looked at different types of histograms to get the feel of different shapes of distributions.

From the mean to one standard deviation above, and one standard deviation below.

I know that's a mouthful. So, you might wanna replay that.

These were the results for Jeremy Lin.

T statistic from this.

You evaluate it at plus 5, which is right here.

Mu is the mean, or the average.

Z scores, then we know what percentage of scores fall in certain ranges.

So it's just e to the, this whole thing over here, minus x minus the mean squared over 2 sigma squared.

So there are the descriptive statistics, or summary statistics.

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

Now what happens when you change the standard deviation.

Here is an interesting data sequence 3, 3, 3, 3, 3.

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

In particular, consider a single data item as our sequence.

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

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.

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

In assignment 1, I literally want you to flip a coin 1000 times.

To see this, recall that a is equal to y bar b x bar, but for a standard score, zₓ always has a mean of 0 and zᵧ has a mean of 0, because we subtracted out their means.

Since on average it didn't move, we just add the mean of its starting position to the no movement, and we get a mean of 0.

And M sub Y. So I'm.

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

If there is a big difference then this is a larger value and we know for the day in question what the mean and the standard deviation is for this percentage change.

It's the quadratic deviation from the mean.

It doesn't resemble the population much at all, and the mean is six, whereas the mean for the population was 5.5.

Let's ask you a different question suppose we're on the fields and we learn how to throw ball.

That's a real easy calculation, right? I would do my body temperature, 100.06 minus the mean, happens to be 100.06, divided by the standard deviation.

So here's a typical outcome for this code.

Squared is the population variance. I'll use SD squared to refer to the variance in the sample and standard error.

If I run it, the mean might be 0.484. There's the standard deviation.

looks like on average, the features x1 has a mean of about 5 and the standard deviation, if you only look at just the x1 values of this data set has the standard deviation of maybe 2.

But overall, the mean of those means or the mean of the distribution of sample means should fall right around the mean of the population.

The square root of 20 is approximately 4.472.

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?

And the correct answer is minus 0.02708 and 0.0256 and this is obtained by taking the mean over here and adding in the standard deviation plus minus up multiplied by 1.96.

Standard deviation of the standard logarithmic distribution

Test are just the average squared error, or one half of the average squared error on my training validation and test sets without the extra regularization chart.

Some people think what's the probability that land within one standard deviation of the mean?

If 1 is the outcome, here is our difference from the mean we square this.