okay [Music] add it up [Music] okay [Music] well, good morning, good morning, happy Monday. I am so glad to see you guys. I know for those of you that were looking forward to yesterday's study group, we decided to move it to today's. It seems that Sunday is not really a good day for some of the people that come and join us, so we'll keep it on Mondays, um, we'll keep it on Wednesdays, and people have um, are liking kind of the Monday, Wednesday, Friday, so we'll just go with that vibe until things change. This is the CompTIA Data Plus um, DA001 study group, so hopefully you are ready to go. Um, I was working on some other work um, that I'm going to be working on and kind of getting the study group together for that as well, having to do with SQL studying, so uh, just be aware that that's on the way. We are going to go ahead um, and get started, just a couple of housekeeping rules for those that are coming in um, a couple of

things one when we start the group. The time frame that we work is in a 45-minute cycle, so we go 45 minutes and then you have a 10-minute break. Typically, this is an hour. This was designed to be a two-hour study group, but it seems that an hour is about the time frame when most people are all, you know, they're good to go during that time, so we're just keeping it to an hour. So you'll get a 45-minute and then we'll get a first break, which is 10 minutes, and then that is really about it. So we don't really get the second cycle, the second 45-minute cycle. We don't really get that. So just want to do the housekeeping rules. Let's go ahead and get started. We're working on Mike Chapel's course and kind of getting our, you know, fee what we want to do with that. The analysts' analysis is at the heart of our work, so we need to understand the difference that we can use. It's not to apply both. As I was listening to

some of the we also need to work to this. I was finding out that there was like the music was overpowering Mike's voice. One of the five key domains covered on the data plus exam. Hi, I'm Mike Chapel, and I'd like to invite you to watch my course on data analysis. It's part of a six-course series preparing you for the data plus exam. I hope that you'll join me as we explore the basics of descriptive and inferential statistics, analysis techniques, and analytic tools. I've designed this series of data plus courses with the beginner in mind. While you'll probably find it a little easier to complete this course and the data certification if you've worked with data before, that's not a requirement. If you're looking to get started in data analytics, this course series will provide you with all the information you need. If you're a technology professional with some data experience under your belt, this course series will help you fill in any gaps in your knowledge and build a solid foundation as you prepare to take the data plus exam.

In this course, we're going to spend a lot of time talking about statistics. Now, I know statistics can be intimidating. I don't want you to worry about that. We're going to walk through. I have not taken statistics. You need to understand for the data. This should be interesting, simple, straightforward language so that you have all of the knowledge that you need to pass the test. Let's start with the very basics. What is statistics anyway? Well, statistics is the practice of applying math techniques to our data in a way that helps us analyze, interpret, and present that data to our audience. The field of statistics has two branches: descriptive statistics. Actually, let's pause for a minute because we do have a question that came in, and I want to answer that question. So, one of the things like where is this coming from. This is LinkedIn Learning, Mike Tapple's course, and LinkedIn Learning. This is a service that is offered through LinkedIn. Now, if you are a veteran, you do have the option to have this free of charge to you if you

have questions about that, you can reach out to me. I'll be happy to show you exactly how to do it. That is also part of your LinkedIn premium services. So, if you have LinkedIn premium, this is a service that you can get free. You can take Mike's course just like I am. We're a group of people that are taking the course, but there was a question of what this is specifically, so I just wanted to put that out there for those that are actually watching and going through the study course. So, let's get back to it. Bribing our data set, they summarize our data and tell us some of the primary visible features that it contains. Inferential statistics go beyond describing our data and begin to draw conclusions from it. We use inferential statistics to make generalized conclusions about our data and make predictions about the future from our data. In this course, we're going to cover techniques of both descriptive and inferential statistics. We're going to begin our study of statistics in the world of descriptive.

statistics. The statistical techniques that we can apply to our data and describe that data to others. We sometimes also describe these as summary statistics because they help us summarize our data sets. The first type of descriptive statistics we'll discuss are called the measures of central tendency. Now, I know that term is a mouthful, but it actually isn't really that complicated. The measures of central tendency are just techniques that attempt to summarize our data with a single value that identifies the center of the data. Now, the question you might be asking yourself is, What does he mean by the center of the data? And that's exactly the right question to be asking. There are three different answers that you can give, and those three answers are the three different measures of central tendency. I'll briefly describe each of them, and then we'll walk through an example of each. We might describe the center of the data set as the average value of the data. If we choose that approach, we're calculating the mean value, and mean is just another term for average. We also might describe the center of the

data set as the middle value in the data set if we sorted all the values in order. If we choose that approach, we're finding the median value of the data set. And finally, we might describe the center of the data set as the value that appears most often in our data. If we choose that approach, we're finding the mode of the data set. These three statistics: mean, median, and mode, are the three measures of central tendency. Let's walk through some examples of calculating the measures of central tendency for a data set. Imagine that I have a class of 10 students, and I measure each of their heights in inches. I record all of these measurements, and then I want to use descriptive statistics to understand more about my data. Here are the 10 values for height. The first descriptive statistic that I'd like to calculate is the mean or average height of my students. I can calculate that using this formula. Let me walk you through these symbols step by step. First, the value that we're calculating is represented by the Greek letter mu. This

is the symbol that we use for the mean value of a variable. It's saying that we're calculating the average value of x, and x is our variable in this case, that's the height of each student. The Greek letter sigma is the symbol for summation, so the top part of this formula just says to add up all the heights. I can plug those heights into the formula here. Then n is the number of observations we've measured, 10 students, so n will equal 10 in our calculation. Then we just do the math. If we calculate this out, we find that our mean value is 32.7. Next, we'll find the median of the data set. Good news, there's no math here. The median is just the middle value of the sorted data set. This data set isn't yet sorted, so let's just sort it so that the values are sorted. Now we just need to find the middle value, but there's a small catch here. This data set has 10 values, so there is no middle. Instead, two values, 31 and 33.

share the middle position. That's no problem. We'll encounter this whenever we have an even number of values in our data set. In that situation, we just calculate the mean of those two middle values to find our median. In this case, that's 32. Now imagine that we had only nine values in our data set. I'll just delete that last value, and now we can find the middle, which is 31. There are four values before 31 in our sorted data set and four values after 31. That makes 31 our median value. Finally, let's find the mode. This is simply the most common value in our data set, the value that appears the most often. It's easier to find the mode if we first sort the data set, and once we do that, we can see the mode here is 30, the only value that appears twice. Now, you sometimes might encounter a situation where there are two or more most common values. For example, look at these modified values. Now the numbers 30 and 35 both appear twice in the data set. That's not a

problem. Either this data set just has two modes, 30 and 35. When you're selecting a measure of central tendency, there's an important thing for you to understand: mean values are heavily influenced by outliers. One abnormally high or low value can dramatically alter the mean. For example, if we go back to our original data set and change the last person's height to be a dramatic outlier at 88 inches, we can now recalculate the mean and the median. The mean now significantly jumps to 38.2, while the median stays the same at 32. For this reason, statisticians often prefer to use median values instead of mean values. The measures of central tendency—mean, median, and mode—help us identify the center of a data set. Now, that's one important descriptor, but it doesn't tell us everything we need to know. Data sets can have the same center but be arranged differently around that center. The measures of dispersion tell us how the data is spread out. As with the measures of central tendency, there are

several different measures of dispersion that we can use, and we'll walk through them in this video and the one that follows. Let's start with the simplest measures of dispersion. First, we have the minimum and maximum values in a data set. These are very straightforward to identify, particularly if our data set is sorted. Here's that height data set that we worked with in the last video. It's already sorted, and we can find the minimum value in this data set by simply locating the smallest value, which is 28. Similarly, we can find the maximum value by finding the largest value, which is 38. We can use the minimum and maximum values to calculate the range of the data set. The range is simply the size of the distribution of the values, and we calculate it by subtracting the minimum value from the maximum value. In this data set, we can subtract 28 from 38 and find that our range is 10. The next measure of dispersion is the distribution of a data set. We get the distribution by computing the frequency with which each value appears in a data

set, and then we often plot it on a histogram. For example, here's the distribution of the height data set that we've been using. We can also call this a frequency diagram. Now, this one isn't very interesting because we have a small number of values, and they're spread out fairly flatly. The normal distribution is a commonly used distribution in statistics because it frequently occurs in the natural world. The normal distribution assumes that data is clustered around the center and has values that taper off evenly in both directions away from the mean. It generates this shape, and people commonly refer to this as the bell-shaped curve. If we know or assume that a particular data set is normally distributed, we can then use that information to draw some statistical conclusions. We'll talk more about that later in the course. In some cases, we wind up with data that is not only not normally distributed but also doesn't fit any of the other distributions used by statisticians. These cases are examples of non-parametric data, and analyzing this non-parametric data requires the use of

special methods that don't rely upon distributions. The last two measures of dispersion that we need to discuss are variance and standard deviation. These values are related to each other, and they give us a sense of how values are spread from the mean. Let's start with variance. The variance is the average of the squared differences of each value in a data set from the mean. We calculate variance with this formula. Now, once again, we have some Greek letters here, so I'm going to walk you through this formula. We saw mu earlier in the course; that's the mean value for the population. Lowercase x is each of the values in the data set. So, we take each value in the data set and subtract the mean from it. Then, we square that difference. After calculating all the squared differences, we add them together and divide by n, the number of values in the population. That gives us lowercase sigma squared, the variance. Now, with that explanation under our belts, let's try calculating the variance for our class height data set. We already know that the mean value for this data.

set mu is 32.7. Let's look at each of our data points from earlier. We first subtract the mean value 32.7 from each of these, which gives us our second column of data x minus mu. Then we square those terms to get our third column of data. Now looking at our formula, we need to add all of those squared values together, which gives us 116.2, and then divide that by the number of values 10 to get our population variance of 11.6. Now I just used the term population variance there, and I haven't mentioned that term before. That's because there are two different ways that we can calculate variance, depending upon whether we have data about a population or data about a sample of that population. A population is when we have data about every possible element of a data set. For example, if our class had 10 students in it and we measured all of their heights, we have data about a population. A sample is when we have data about a representative portion of that population. Maybe our class had 100

students, and we randomly selected 10 to measure. If that's the case, we need to change the math slightly to calculate a sample variation. Now, before we do that, let me take a little divergence here to clarify some symbols for you. There are actually different symbols for size, mean, variance, and standard deviation, depending upon whether we're dealing with a population or a sample. Here are the symbols you've already seen for the population. When we have a sample, instead of using capital N to represent the population size, we use lowercase n to represent the sample size. Instead of using the Greek letter mu to represent the population mean, we use the symbol x bar (x with a line over it) to represent the sample mean. And instead of using sigma squared for the population variance and sigma for the population standard deviation, we use s squared for the sample variance and s for the sample standard deviation. Now, I'll be careful to explain these terms again when we encounter them, but you might want to memorize this small chart to help you keep things straight. So, back to variance.

before I have to make sure that we write that down variance um because I'm sure that's probably going to come up somewhere on the test but we'll figure it out by lower case n minus 1 to get our sample variance. So if our class height data was a sample, the variance would be 12.9 instead of 11.6. Again, rewrite the sample variance as s squared rather than lowercase sigma squared. All right, with all that math under our belts, we can move on to the last measure of dispersion, the standard deviation. Fortunately, this one is easy to compute. It's just the square root of the variance. Here are the formulas. The population standard deviation is the square root of the population variance, and the sample standard deviation is the square root of the sample variance. So for our class data, if we had data about the entire population, the standard deviation would be 3.4, and if our data was about a sample of the class, the sample standard deviation would be 3.6. The variance and standard deviation

provide us with a good way to measure the dispersion of an entire data set. But what if we want to measure how different one value in our data set is from all the others? Z-scores provide us with the ability to do this by describing how many standard deviations a particular measurement is away from the mean of the data set. We calculate z-scores using a few of the values that we've calculated already: the mean and the standard deviation. To get the z-score for a particular measurement, we first measure the distance it is away from the mean by subtracting the mean from it. Then we divide that result by the standard deviation to express the distance in terms of standard deviations. Now, I use the symbol sigma here for a population standard deviation, but this formula works the same way for a population or a sample, as long as you plug in the appropriate standard deviation value. If we look at our table of heights, we already know that the mean height in this table is 32.7 inches and the population standard deviation is 3.4. So

Let's calculate the z-score for each one of these measurements. First, we calculate how far each measurement is away from the mean, and then we divide those values by the standard deviation, which provides us with the z-scores. For example, if we look at the first row, we see that a height of 38 inches is 5.3 inches away from the mean, and that's 1.56 standard deviations above the mean, giving us a z-score of 1.56. Similarly, on the next row, a height of 30 inches is 2.7 inches below the mean. That gives us a negative z-score because the value is below the mean, so we get a z-score of negative 0.79. When we have normally distributed data, we can also make some assumptions about our data. In a normal distribution, 68.2 percent of the data lies within one standard deviation of the mean, meaning that z-score is between negative one and positive one. Ninety-five point four percent of the data lies within two standard deviations.

of the mean, giving it a z-score between negative two and positive two, and ninety-nine point seven percent of the data lies within three standard deviations of the mean, with z-scores between negative three and positive three. Z-scores above or below three represent possible outliers, and we shouldn't expect more than three in a thousand values in a normally distributed data set to have z-scores below negative three or above positive three. We've all seen percentages throughout our lives. You might see statistics such as ninety percent of all people live in the northern hemisphere, or you might see percentages used to describe a sale at a store. All prices are 50% off today. Percentages are very commonly used in the world of statistics to describe our data, and the word percent translates literally to by the hundred, and it's a statistical technique used to normalize our data by scaling a measure to be a fraction of 100. When we calculate a percent for our measure, we take the number of items that are affected and divide that by the total number of items. We then multiply

that value by 100 to get the percentage. For example, suppose that we rolled this set of ten dice. We can look at these results and see that three of the dice are showing the number one. That's three out of ten or thirty percent. We very often use percentages to describe the proportion of a population that has a certain characteristic. We can also use percentages to describe how values change over time. We can use the percent change to compare old values to new values when we calculate percent change by subtracting the old value from the new value and dividing it by the absolute value of the old value. We then multiply that result by one hundred. These two bars are the no no. I don't expect foreign. I don't expect for you guys to get this the first time through. We can use um especially if you have not done statistics in a while. Different from each other uh but this is going through part of the course using a more complicated formula. This is of course just a quick summaries like two-minute videos. The value of that calculation and multiply it by a hundred.

Let's look at an example of each of these calculations. So, I am going to pause for a second to answer another question that was asked. So, no, this is not something that I expect for you guys to get like really quickly. So, um, I'm not getting it very quickly. I'm going through the quest work to see what it is. And then once we get done with this, what we will do is proceed to the book, um, which we have the book, um, in a digital form in the Kindle. I did put that inside of the last stream. So, we will start the book after this, uh, so that we can go through. And what we will do is we will tie them both together as we prepare for the studies. But right now, I believe that this is just a great overview of the content. So, we get a chance to be able to just look through it and say, Okay, this is what, you know, what we need to prepare for. So, we will go through some statistical work, but we just need to finish the preparation for this first to make sure.

that we are ready, so I just wanted to address that before we proceed forward. I receive a raise of 15,000, making my new salary 115,000. I want to measure that change. Now, this is comparing a new value, 115,000, to an old value, 100,000. So, it's a problem where we should calculate the percent change. We take the formula for percent change and plug in the data, and after crunching these numbers, we learned that there was a 15% positive change to my salary. Now, let's try another example. Let's say that I have five dogs and you have three dogs, and I want to measure the difference between us in the number of dogs. This isn't a problem about change; my dogs didn't change into your dogs. It's a problem about difference. So, I use the formula for percent difference. I plug all the data into that formula, and I learned the percent difference is that I have a 50% difference between the number of dogs that I have and the number of dogs that you have. That's how we can use

percentages in statistics. [Music] All right, what symbol is used for the variance of population and data is the question. I believe that it is this one. Analyze the values of x shown below. What is the range of these values: two, three, four, five? It said range. Now, I could be because if we're just going one, two, three, four, five, so there are five, and that's the total range. That's an easy question. What is the modal value? The modal value, I believe, is five. Could be wrong, but okay. So, if it's going, what is the mean, median, and the mode, then it would actually be seven, I believe. No. So, if it's one, two, three, they're saying the modal value. I don't believe the modal volume because if you were to do five, and then there are five of them, it can't be right, though. So, it is two. Okay, so I'm assuming that what they did was take the five. I'll have to look at the modal value again, but let's move on to the next.

question: You are measuring how much a child has grown over the past year and would like to express that using a percentage. What calculation is most appropriate? I'm gonna go percentage change. Analyzing a data point, you find that the point is one standard deviation above the mean. What is the z-score for that data point? So, that will be one above, I believe it is, I think it's like here, then positive side. Okay, so it said one above the standard deviation. So, okay, let's move on to the next. We've already talked about how sample data allows us to work with a small subset of a population when we don't have data available for the entire population. When we work with samples, we're working with approximations of actual statistical measures of the population. For example, if we measure the heights of a sample of people from a large population and calculate the mean height, the value we get is the mean height of that sample. We hope that the sample mean is close to the population mean, but our measurement won't be exact because we didn't use all

of the data. Confidence intervals allow us to estimate how close a sample mean might be to the actual population mean. Confidence intervals are a powerful tool that allows us to put bounds around our estimates. Here's the formula for computing a confidence interval for a sample. You've already seen all the elements of this formula individually, so now we're just putting them together in a different way. Let's walk through them. X bar is the sample mean, while sigma is the population standard deviation. N is the number of elements in the sample or the sample size, and Z is the z-score parameter for the critical value. That's a value that we plug into an equation from a table where we look up the value depending upon how confident we need to be in our results. The more confident we need to be, the wider the range of the estimate will be. Here's that table of critical values as an example. If we want to calculate a 95% confidence interval, we use a critical z value of 1.960 in our formula. So, let's try an example. We measured the

mean of our height data set. We calculated it to be 32.7 inches. The population standard deviation for that data set is 3.4, and we had a sample size n of 10. Let's say that we want to construct a 95% confidence interval, so our z value is 1.96. If we plug these values into the equation, we get a range of 30.6 to 34.8. This means that we can be 95% confident that the true population mean is somewhere between 30.6 and 34.8. Now I'll end our conversation about confidence intervals with an important note. In the formula I just showed you, we use the population standard deviation sigma to compute the confidence interval. The reality is, in many business problems, we don't actually know the population standard deviation because we only have data about a sample. In those cases, we can use the sample standard deviation s as an approximation of the population standard deviation. One of the more common tasks in statistics is to come up with a possible

idea conduct a survey or experiment to test that data and then analyze the results. In these cases, we're working with a sample of the actual population and trying to determine whether the evidence we've gathered from our sample points to a statistically significant result in the real world. First, we need to come up with our hypothesis, the idea that we're testing. In the world of inferential statistics, we had the underlying idea that it's difficult to prove that something is true, but we can disprove something by finding a counterexample. We do this by having two different hypotheses. We take the statement that we're trying to prove is true and call that our alternative hypothesis or H sub A. Then we take the opposite statement and call it the null hypothesis, H sub zero. We then look for evidence to disprove the null hypothesis. The null hypothesis is usually the idea that there has been no change. Let me give you an example. You do that in scientific testing, a new drug actually. So that's quite interesting to identify whether the drug would be effective in

the general population. We formulate our alternative hypothesis, the thing we're trying to prove, as the concept that the drug has a statistically significant effect on the population. Then our null hypothesis is that the drug has no effect on the population. We then work to disprove the null hypothesis to show that the drug works. Now before we can come to any conclusion, we also need to decide upon the level of significance that we want to have in our test. That's the probability that our testing will say that the null hypothesis is wrong when it's actually correct. That type of mistake is known as a type 1 error. We express the level of significance as a probability using a measure called alpha. If we want our test results to have a 95 chance of being correct, then we want a 5 chance of incorrectly rejecting the null hypothesis. So we use an alpha value of 0.05. Once we've decided upon our null and alternative hypotheses and our alpha value, we go ahead and collect our sample. We do this by observation, survey, or

experiment with that data in hand. We run a statistical test that produces an output known as the p-value. The p-value is the likelihood that our results are not statistically significant and just occurred by random chance. We use the p-value to decide whether to reject the null hypothesis. We do this by comparing the p-value and our selected alpha value. If the p-value is less than or equal to the alpha value, we reject the null hypothesis. This means that we can conclude that the alternative hypothesis is true within the degree of statistical significance that we specified in our alpha value. If the p-value is greater than the alpha value, we fail to reject the null hypothesis, and we do not have the evidence we were seeking. So back to our drug testing example, let's say that we run our statistical test, and we determine that the p-value from our test is 0.02. In that case, the p-value of 0.02 is less than our alpha significance level of 0.05, so we can reject the null

hypothesis and conclude that the drug is effective. That's a simple example of hypothesis testing. Now, you probably noticed that I didn't tell you how we get the p-value or how we conduct those statistical tests. I'll explain that in the next couple of videos when we explore t-tests and chi-square tests. Before I do that, I want to return for a moment to the concept of errors. I already explained to you the idea of a type 1 error, but let's look at all the possible outcomes of a statistical analysis. When we run an experiment, we can come to two conclusions: we can accept the null hypothesis, or we can reject the null hypothesis. Then, in the real world, there are two possibilities: the null hypothesis is true, or it's false. In cases where we accept the null hypothesis in our analysis, and the hypothesis is true in the real world, we've come to a correct conclusion. Similarly, if we reject the null hypothesis and it's false. Interestingly, we've seen this box before.

these boxes, and it's actually true. That's the type 1 error that we've already discussed. On the other hand, if we accept the null hypothesis and it's actually false, that's a type 2 error. The first type of statistical test that you'll need to know about for the data plus exam is the t-test. The t-test is used to determine if there is a statistically significant difference between the means of two groups. It's used to produce a p-value when you're conducting hypothesis testing. You generally use a t-test when your null hypothesis is about a numeric value. Let's look at an example of this t-test for numeric values. Earlier, you might want to prove that a drug raises a certain blood test score by a significant amount. In that case, your hypotheses are about the blood test score, and those values are numeric, so a t-test is appropriate. Your null hypothesis would be that there is no effect, or in more formal terms, that the mean blood test result of the group of people treated with the drug was not significantly different than the

mean blood test result of the group of people who were not treated with the drug. Your alternative hypothesis would be that the drug does have an effect and that the mean blood test result of the group of people treated with a drug was significantly higher than the mean blood test result of those who did not receive treatment. Now, sometimes we need to conduct testing of values that are categorical rather than numeric. In those cases, we can't use the mean because the values aren't numeric. Instead, we're trying to see if two categorical variables are associated with each other. The chi-square test produces a p-value in these situations. Now, the CompTIA exam objectives for Data Plus write out this term C-H-I using the standard English alphabet. Chi is actually a Greek letter that uses the symbol shown here. You might see this either way, so be sure that you know the Greek letter chi. You generally use a chi-square test when your null hypothesis is about categorical variables. When we get ready to study this portion or statistical university data, we're

gonna have to make sure we really go through this: the public or high school and whether they earned no honors, honors, or high honors in college. We might want to know whether there's an association between the type of high school that each student attended and their honors performance in college. These are both categorical variables, so a chi-square test is appropriate. The null hypothesis in this case is that there is no association between the two variables, or in other words, that the type of high school a student attended and their honors performance in college are independent. The alternative hypothesis is that the two variables are associated and they are dependent upon each other in some way. There is a relationship between the type of high school that a student attended and their performance in college. As you prepare for the data plus exam, you won't have to worry about actually performing these tests. While you do need to know how to compute descriptive statistics such as mean, median, mode, variance, and standard deviation, the exam objective for inferential statistics is different. You only need to be able to explain the

purpose of inferential statistical methods such as t-tests and chi-square tests. Correlation is a statistical measure of how closely related two variables are to each other, or in other words, two variables that are correlated will have a strong relationship so that when one variable changes, the other changes as well. As a simple example, consider two variables about people: their height and their shoe size. Now, you can't directly determine someone's shoe size from their height, but the two variables are related. As someone's height increases, their shoe size generally increases as well. That example of shoe size and height is an example of a positive correlation. Positive correlations exist between two variables when an increase in one variable is associated with an increase in the other variable. We can also have negative correlations between two variables. When two variables are negatively correlated, they're still related, but the relationship goes in the opposite direction. When one variable increases, the amount of the other variable decreases. For example, there is normally a negative correlation between the number of classes that a student misses and their grade on the final exam in that course.

as absences rise, the final exam grade falls, and then in some cases, variables simply aren't correlated. They both exist, but there's no relationship between them. There's no correlation, for example, between a student's height and their performance on the exam. Take a moment to look at each of these graphs that you see here. The shapes of these graphs show the different types of correlations. When you see a line going upward, that's a positive correlation, and when you see a line going downward, that's a negative correlation. When you see no trend, there's probably no correlation. We can also describe correlations using a numeric measure called the correlation coefficient. This value, which uses the symbol r, ranges from negative one to positive one. A positive value represents a positive correlation, a negative value represents a negative correlation, and a value of 0 represents no correlation. Now, you won't have to compute r values on the exam, and the reality is that most people never compute r values by hand. Instead, they use statistical software to perform these calculations for them. One last note that's really important.

for you to understand, correlation does not imply causation. Just because two variables are correlated with each other, that doesn't mean that one variable is causing the change in the other. The classic example of this is a data set about sunburns and ice cream consumption. If you just looked at these two variables, you'd probably find a correlation between the two. As sunburns increase, so does ice cream consumption. Now, that might lead you to believe that eating ice cream causes sunburns. That's certainly not true. The reality is that both of these variables are correlated, but they have a cause that's outside our initial picture. Hot sunny days cause both sunburns and ice cream consumption. Correlation is not causation. When two variables are correlated, we can use that correlation to make predictions about one variable from the other. Simple linear regression models identify the formula of a straight line that moves as close to our data as possible. This is a very simple prediction tool, but it's also very effective when the relationship between two variables is

simple for example. Here's a data set showing the rate of skin cancer deaths in U.S. states. On the x-axis, we see the latitude of the state, so lower latitudes appear on the left side of the graph and higher latitudes appear on the right side. On the y-axis, we see the number of deaths in each state. Just looking at this graph, we can see that there is a negative correlation between latitude and deaths. As latitude increases, deaths decrease. That makes sense because higher latitude states are further away from the equator and experience colder weather, so people go out in the sun less. If we want to go beyond this correlation and examine the relationship in more detail, we can use linear regression that plots a line on the graph that you see here. The line shows us the prediction that we would make using our simple linear regression model. The line has a formula that we can obtain from a statistical analysis package. In this case, the formula is deaths equals 389 minus six times the latitude. We can use this formula to make predictions. Let's

say that we wanted to predict how many deaths would occur in a state with a latitude of 30. We could plug that into the formula and find that we'd expect about 209 deaths, as represented by the blue dot placed on the line. Similarly, if we wanted to predict the deaths in a state with a latitude of 45, we just plug that number into the formula and find that we'd expect about 119 deaths, as shown by the green dot. Simple linear regression is just one technique that we can use to make predictions about our data, but it's limited by the fact that it can only make predictions along a straight line. As you continue your studies of data analysis beyond the material covered on the dataplus exam, you'll learn many more advanced prediction techniques that can make more complex predictions. All right, so let's see if we can answer the set of questions we have about three minutes before you go on your break. So let's see what we have. You would like to know whether the mean height of a group of children is

statistically significantly different from another group. What statistic tests would be most appropriate? Okay, let's see. I don't know. So then it would be a t-test then, yes? Yep, okay. What output from a statistical test is used when performing hypothesis testing? I don't know this one. P-value. The answer to the question is p-value. What output from a statistical test is used when performing hypothesis testing? It is p-value. What technique can you use to predict one value from another using linear relationships? Correlation. The question would be regression. Okay, which one of the following r values shows the strong positive correlation between two variables? All right, so we got that done and answered those questions. And before we go forward to the next one, you go on a break in about a minute. Um, so what we'll do is go ahead and um, get prepared for our break. So go get you some coffee, water, that type of thing, check your email and stuff. You'll know when we're on break because the system will automatically go into break. There's going to be a if this is your first time

here. There is going to be an area where it just kind of goes into like a storm. You'll hear like rain and thunder and that type of thing that lets you know your own break. And then there's a countdown that's there. You'll hear music and stuff like that. So just go ahead and do that part. I will get us amped up and ready for the next part, but we won't go into that. We will come back to that in a bit. But after we get done with this, we have about 15 minutes left in the study course. So we'll just wrap things up with these last couple of classes, go through with this last test quiz rather, and then we should be pretty ready to go and to move forward. So enjoy your break. I'll see you guys back here in roughly about 10 minutes. If there is anything that you have so, so, so all right. So you guys are on your way back here in a couple of seconds. We're gonna be back. We're gonna finish up. It is we

basically have about five minutes um before the coursework will end anyway. So what I just decided that I would do for those that are back a little bit early is we won't start the next section um. We'll just go ahead and head out for the day since there is uh not anything else we have this section over here that we would need to go into again. We only have roughly about um about five minutes left. So I'll go ahead and give that five minutes back to you guys so that you know because otherwise I mean I guess we could just go through this and then move on and whatever time is left. We'll just analytically hem it out but we need to understand the business objectives and the desired outcomes. This understanding informs the type of analysis that you'll want to conduct. The first step to understanding business objectives is to ensure that you understand the business questions at hand. The goal of answering a business question is to develop an insight that informs a business decision. Now these business questions come in many forms. You may receive questions

informally through hallway conversations, text messages, or emails. More significant initiatives should have written requirements documents defining the business questions that are in scope. Regardless of the form that your requirements are in, you need to review the business questions and identify any points that require additional clarification. This will help you identify the data that you need, as well as the data sources required for your analysis. When you're reviewing requirements, develop a list of clarifying questions to probably make myself smaller. I don't need to be so large, and it can also identify any gaps between the data and resources that you have and those required to complete the analysis. For example, one of your requirements may be to analyze sales data for the past 10 years. However, due to a change in the system that records sales, you might only have access to seven years of historic information. The absence of data over a three-year period is a gap that you need to discuss with your business partners. Once you have your list of questions, review it with the business sponsor to ensure that you agree on expectations. Recognize that reviewing and refining

business questions is an iterative process. While you need to have initial clarity, you will likely need to return to your sponsor for additional clarification as you begin and work through your analysis. Once you have consensus around the scope of your analysis, clarity around any open questions, and you know what data you need and where it's coming from, you can proceed confidently with conducting your analysis. It's a good idea to maintain your requirements document as you go about your work. Use the document to track new issues that impact you. Do this in project management too, where you have a change order deliverables. A running log identifying any scope changes is a valuable aid that can help you make sure you deliver your analysis accurately and on time. It can also help you after your work is complete as you reflect on what went well and what would make future projects more successful. When you first encounter a new data set, all right, this should be the last one close to three minutes and give you context for further analysis. While there are many different approaches to conducting an EDA, they

typically encompass six different steps. First, you should check the structure of your data. Ensure the data is in the correct format for analysis. Most data analysis tools expect data to be in tabular format, so you need to confirm that your data has defined rows and columns. Second, check the data representation. Become familiar with the data. In this step, you validate data types and ensure that variables contain the data that you expect them to contain. Next, you can explore missing data. Check to see if any data is missing from the data set and determine what you should do about it. When you're checking for null values, calculate the proportion of each variable that's missing. If you discover that most of the data you need is missing, you need to either categorize it as missing or impute a value for missing data. You can also go back to the source and remediate any issues that occurred during data extraction. After you identify any missing data, move on to identify any outliers. These outliers are observations of a variable that deviates significantly from other observations of that variable. As you've

learned outliers can dramatically impact some descriptive statistics such as mean. It's best to determine the cause of outliers and consider whether or not you want to leave them in the data before proceeding with your analysis. Once you have a clean data set in hand, compute summary statistics for each variable. For numeric variables, examples of summary statistics include mean, median, and variance. For categorical data like eye color, you could develop a table showing the frequency with which each observation occurs. Finally, check your assumptions. Depending upon the statistical methods that you're using, you need to understand the shape of the data. For example, if you use techniques that assume a normal distribution, make sure that your data is in fact normally distributed. As you continue beyond exploring, that is, you'll probably want to use that is all for today. So I appreciate you guys hanging out. Uh, we went through about an hour and quite a few of our areas here getting into statistics and this portion. So we will pick up again on Wednesday. Um, if there's anything that you guys need, you can of course reach out to me. Let me

know, and I will see you guys on Wednesday. I appreciate you hanging out and chilling with me. And you know what? We'll do this coming up soon, okay? Later, foreign.

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