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

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

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

There's variance in the sample SD squared.

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 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.

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.

Std. deviation

Std dev.

Deviation

Std. dev

Standard deviation

standardDeviation

Standard Deviation

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

So here's a typical outcome for this code.

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

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.

Mean value of the standard logarithmic distribution

So there are the descriptive statistics, or summary statistics.

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

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.

Standard deviation of the standard logarithmic distribution

Standard error is this distance right here.

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

Let's now consider linear regressions of standard scores.

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

Standard deviation of the distribution

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

Sample standard deviation

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.

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

STD is the standard deviation of the distribution.

Standard deviation of the normal distribution

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