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

Mu is the mean, or the average.

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.

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

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

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

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.

Standard error is this distance right here.

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

Now what happens when you change the standard deviation.

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.

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.

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

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

T statistic from this.

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

So here's a typical outcome for this code.

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

Mean

Average value

Mean

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

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

These were the results for Jeremy Lin.

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

So the T statistic that we could derive from that is going to be our mean, 17.17 minus the true mean of our population.

There's variance in the sample SD squared.

Average bitrate value

So what is the mean over here?

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

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

Size, set the feature

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

So there are the descriptive statistics, or summary statistics.

If we say z is this thing in here, z is how many standard deviations we are from the mean, z score squared.

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

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

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

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.

The variance is the average squared distance from the mean, the standard deviation is the square root of that.

And if you will verify them, you will find that the maximum likelihood estimate for sigma squared is the average deviation of data points from the mean mu.

Mean Removal