This is top 10 topic number eight, which is very ancient creates uncertainty star, the sister to page through it Sam redo of the statistics of whether the presentation through to the and we will hustle down here in two PowerPoint slide number on me a second here to find a PowerPoint slide number eight is fixed in the top 10 cons of memory is slight and 93 to the end of the presentation of okay recall we talk with talk about descriptive statistics inferential statistics and in industry descriptive statistics, we computed the measures of central tendency like to mean and the measures of dispersion like standard deviation of pain and standard deviation is to square root of the variants very in store for variation is dispersion. All of the day to them a end in this topic is about how that dispersion creates an order is related to uncertainty on a continuum between containing a perfectly certain on one side and perfectly uncertain on the other side most of our work lie somewhere in the middle if it was perfectly certain we probably would study it because we would know the answer already fits perfectly up that would be order and and if it was perfectly uncertain that would be chaos of all leaves some of our work is somewhere in between a pain but variation creates uncertainty and will did not give you a couple of examples here in a moment the next two slides to that McPherson first life's like 90 for a know very it should so in this particular tissue of certainty which he should have exact prediction or, excuse me exact prediction or understand her at an explanation of of what you see, who pay the standard deviation is zero for example, if you say you have a of four numbers 333 in three in a perfect certainty is that the standard deviation is zero. Also the third bowl the variances to zero or four if all data is exactly the same obtained for example, all workers in a minimum-wage job or workers at a job with the same wage. They're it to did there's no deviations of this nothing to measure in terms of uncertainty. There are at least good for that particular question, what is so waged away just the same for everybody came next slide on the other second end of this ski and the other end of the communities have high variation. High variation in the first blow point is uncertainty or unpredictable out if it's unpredictable we don't be since there's a high amount of uncertainty without a high degree of part of an predictability and also a high degree of in expert. We cannot explain that David E. there's not predictable, not explainable. It's not very useful if those are there those are characterized by high degrees of standard deviation and another is a relatively high standard deviation as opposed to zero something a high variance high standard deviation for example, the two examples on the slide the workers in downtown LA have variation between the salaries for the CEOs and the sours of the garment workers at the Sauers of the CEOs of the fairly high this hours ago, workers would be fairly low second example the of the in New York temperatures and all I can relate to. I've been there in New York temperatures in the spring range from below freezing to very hot within a lead as it transitions to some are okay so the variations is pretty high up there with them within that particular sample, which is a particular a range of a couple of months. Take so one way we do that is, we compare standard deviations for the temperature example before it is one example heart, it's hard to come up slow. One of the variations of a couple of examples sample of point number two in a beach city like in Redondo Beach or Santa Monica, a small standard deviation means the single temperature is called reader reads close to the mean if if the standard deviation is fairly low. That means most of the data is near the mean to remember the standard deviation is on average to distance the war of the average distance the points are away from the Main as opposed to say a high desert city like Lancaster for example, to excuse me as a heist of relatively high standard deviation and has hot days and cool nights for example. So in that particular in case some of the data points are further way both positive and negative in terms of distance. There are in terms of to the left to the right of the mean of all, on a scale, the there are more points better towards the hot and towards the cool even though the means may be the same mean maybe the same as the Beach city states that the comparison of standard deviations. As we need both the mean and standard deviation tip to describe a sample well. Okay, one idea related to to those two ideas is the standardbearer of the maintenance, harder membership to say to yourself and concentrate and work, and the formula is pretty easy, but it's difficult to remember sometimes is called the standardbearer of the main Senator of the mean as the slide says were an slight 97 is the standard deviation of the sample mean the standard deviation of the sample mean to the standard error of the Main is equal to the standard deviation divided by the square root of an list and never error the meme is related to the standard deviation. But what we divided through by the square rid of them in other words, the denominators can make it larger as and gets larger, not as fast as them does because is just the square root of them, but he does get larger for example, the standard deviation is 10 and the sample sizes for that would mean the standard error of the mean is 10 divided by the scorer for witches to 10 divided by two is five note that five is less than 10 so the standard error of the mean is less than the standard deviation, which makes sense for taking the standard deviation and dividing it by some note also that as in increases in other words also the square root of them would also increase as the denominator in a fraction increases. The standard error of the total amount decreases the number of the deepest phenomena gets larger the total number to smaller so as any increases the standard air decreases locate another important topic related to very a nation is something called the sampling distribution and sampling distribution is the expected value is the expected value of the sample mean we would hope equals the population mean, but an individual and one individual sample means could be smaller or larger than the population may mean it's sure what an individual sample means could be the same as the population mean, but it's probably smaller early larger by some amount who can't in bullet point number two of the men that put the population mean is a constant parameter, but the sample mean is a random variable and explain the sentence again remember when talking about the population were talking their parameters for US samples were talking about statistics, but remember of the population is it typically known. And even if we do know the population we usually don't know the standard deviation actually so its its its fifth think of it this way the pop the parameters in the population are fixed about are no the only thing that we can see is an individual sample or in some cases multiple samples of a population population mean is a constant parameter constant but unknown parameter, but the sample mean is a random variable of a especially if we selected well in the UK there will appoint in such soaps so the sampling distribution is simply the distribution of the sample means for example, if I had a population of some numbers, and I pulled out a sample and I computed the meanest 12 that's that's one mean that the sample mean of 12 for one sample. If I take that same population drop another sample of those simple meme might be 13 or 13.5. If I take another sample, it might be the a 12.2. If I take another sample, it might be 11.8 I think another sample it might be 12 again to take another sample it might be 11.4 so as you take different samples you can compute all the sample means. If you plot all of those sample means you get a sampling distribution of sampling distribution that's the third bullet here on slide 98. A sampling distribution is the distribution of all of the sample means that you compute if you compute if you poll more than one sample, and example on page on slide 99 the mean age of all students in the College of business building is the population being okay to the mean age of all the students in the building as the population means probably should be all students in the culture business but was close enough are right this second bowl, but each classroom is a sample in the right. There's lots of classrooms in the bill to a meet in the the the the the building is in in this example the building as the population named second bowl of each classroom is a sample mean assuming the samples are our are what are called independent and identically distributed by them what it means that the fancy name for it just means the samples are pulled from the Pope from the population in the same way each classroom is a sample name and pages like as said before a war of the ages might be 30 233-2620 7 1/2 etc. etc. full point number three the distribution of the sample means from all of the classroom so say about 20 classrooms is called the sampling distribution and if it am the last slide in this particular section is something known as the central limit there and the reason that's important is it is because the link between the sampling distributions is our link. It is the link to the central limit distribution and the Central limit distribution is important because that's the key concept in inferential statistics that allows us to take a look in the sale will take a look in the sample and draw inferences about the population to bullet point number one if the population standard deviation is known to the sampling distribution of the sample means is normal if and this is the sample size and is him is larger than there are about larger than 30 ads about the magic member some people just debate that particular murder of the best number you learn in class stuffed the population standard deviations and sound sampling distribution of the sample means is approximately normal. You'll see that word all the time it'll say a problem will say of sample was drawn from a normal distribution or approximately in normal distribution. Assuming the sample is larger than about 30 or so, which most are many are low point number two of the central limit their applies even if the original populations skew okay, which is nice of so the Central limit even if even if the mean to and the standard deviation, and even if you were to plot out one individual sample even if the original population is queued in the you can still use when you when you poll multiple samples in it and you plot out the sample distributions you can still use the Central of up there and it still applies even though the distribution of one particular sample doesn't seem to look normal. The distribution of the sample means will be approximately normal, which is nice to know students forget that all the talk and