# Standard deviation and mean relationship poems

### Statistics Poetry | Statistics Help @ Talk Stats Forum

to capture this relation: first, intuitively, by discussing examples of poetry The numbers represent the average strength of association of the .. Notably, the poems have a standard deviation similar to the factual texts, indicat-. Variability - Standard Deviation, Variance, Range, IQ Range: Variability measures . "Mean" is modified slightly (and therefore I've put it in quotes) to involve. Mean, Mode, Median, and Standard Deviation. The Mean and Mode. The sample mean is the average and is computed as the sum of all the observed outcomes.

And they also wanna have a sense of the spread around that central tendency one year after graduation. So they all agree to put in their salaries into a computer, and so these are their salaries. They're measured in thousands. So one makes 35, 50, 50, 50, 56, two make 60, one makes 75, and one makesSo she's doing very well for herself, and the computer it spits out a bunch of parameters based on this data here. So it spits out two typical measures of central tendency.

The mean is roughly The computer would calculate it by adding up all of these numbers, these nine numbers, and then dividing by nine, and the median is 56, and median is quite easy to calculate. You just order the numbers and you take the middle number here which is Now what I want you to do is pause this video and think about for this data set, for this population of salaries, which measure, which measure of central tendency is a better measure?

All right, so let's think about this a little bit.

### Mean and standard deviation versus median and IQR (video) | Khan Academy

I'm gonna plot it on a line here. I'm gonna plot my data so we get a better sense and we just don't see them, so we just don't see things as numbers, but we see where those numbers sit relative to each other.

So let's say this is zero. Let's say this is, let's see, one, two, three, four, five. So this would bethis is 50,, and let's see. Let's say if this is 50 than this would be roughly 40 right here, and I just wanna get rough. So this would be about 60, 70, 80, 90, close enough. I'm, I could draw this a little bit neater, but, 60, 70, 80, Actually, let me just clean this up a little bit more too. This one right over here would be a little bit closer to this one.

Let me just put it right around here. So that's 40, and then this would be 30, 20, Okay, that's pretty good.

So let's plot this data. So, one student makes 35, so that is right over there. Two make 50, or three make 50, so one, two, and three. I'll put it like that. One makes 56, which would put them right over here. One makes 60, or actually, two make 60, so it's like that. Risk is one reason to make decisions about what to buy.

Risk is a number people can use to know how much money they may earn or lose. As risk gets larger, the return on an investment can be more than expected the "plus" standard deviation.

## Mean and standard deviation versus median and IQR

However, an investment can also lose more money than expected the "minus" standard deviation. For example, a person had to choose between two stocks. Stock A over the past 20 years had an average return of 10 percent, with a standard deviation of 20 percentage points pp.

Stock B over the past 20 years had an average return of 12 percent but a higher standard deviation of 30 pp. Thinking about the risk, the person may decide that Stock A is the safer choice. Even though they may not make as much money, they probably will not lose much money either.

The person may think that Stock B's 2 point higher average is not worth the additional 10 pp standard deviation greater risk or uncertainty of the expected return.

Rules for normally distributed numbers[ change change source ] Dark blue is less than one standard deviation from the mean. For the normal distribution, this includes Most math equations for standard deviation assume that the numbers are normally distributed.

### Standard deviation - Wikipedia

This means that the numbers are spread out in a certain way on both sides of the average value. The normal distribution is also called a Gaussian distribution because it was discovered by Carl Friedrich Gauss.

**Mean and standard deviation versus median and IQR - AP Statistics - Khan Academy**

Numbers are not normally distributed if they are grouped on one side or the other side of the average value. Numbers can be spread out and still be normally distributed.

The standard deviation tells how widely the numbers are spread out. Relationship between the average mean and standard deviation[ change change source ] The average mean and the standard deviation of a set of data are usually written together. Then a person can understand what the average number is and how widely other numbers in the group are spread out.

The way a group of numbers is spread out can also be given by the coefficient of variationwhich is the standard deviation divided by the average.