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Part 1 - Lean Six Sigma Green Belt Introduction Video

6. Measures of Central Tendency & Dispersion

If data is given to me, what do I do? First, I need to perform simple measures. What are those? Let's look into first measures of central tendency. We talked about population and sample. The notations used and the formula used to calculate each one of these would differ a little. So please pay attention. There are three measures of central tendency. One is mean, one is median, and the third one is mood. For a population, you represent it using new The population mean is represented by new. It's the sum of all the numbers divided by the number of numbers you have in the data set. All right. You see Greek letters primarily for population. If it's a sample, you represent me or the average as an x bar, which is also the sum of all the variables divided by the number of variables. It's denoted by a small m because it's not the complete population, it's just a sample of the population. The mean is affected by the outliers, basically. Hence, you can probably look into median. Median is the middle value of the data. Let me explain this. Let us first look at the mean or average. If I have numbers 1234 and 5, If I take a simple average of this, how would I calculate one plus two plus three plus four plus five, which would be 15? I would divide that by the number of digits that I have. Sorry, for the count of this, I have five numbers here, so I divided by five, which is three. The mean is three. In this case, take another data set. Say I have the numbers 1234 and then 50. What would the count be? What would the summation of these numbers be? That will be 60, and since there are 51234five numbers, I divided by five, and the mean is twelve, and the mean here is three. The difference is only one number, 50, which raises your average significantly, right? This is called an outlier. Basically, a number that is extremely low in comparison to the rest of the numbers or a number that is extremely high in comparison to the rest of the numbers If you have such outliers, modelling would not be a feasible option. What do you do? You investigate the median or more. What is "median"?It is the middle value of the data. Say I have the numbers 123-4. The median in this data set would be three because that is the middle number. Or you can simply calculate using a formula. Also, if I have n numbers, I have five in this case. So I do five plus one divided by two, which is six by two, which is three. The third number is the median, and this is the third number. n plus one divided by two is the formula. Basically, n is the number of numbers that I have in the data set. In this case, medium is fine, right? Extremely easy. What if I have an even data set? Yeah. Now what do you do? It's simple. Take the average of the middle numbers because there is no middle number here. So I take the average of these two, that is, three plus four divided by two, which is nothing but seven by two, which is 3.5. So the median in this case would be 3.5. Let me ask you, what is the median of this data set be?Would it be nine? Will you be right and correct in saying so? Answer: no. You will have to arrange these numbers in ascending or descending order. Let me arrange 12367, nine and ten. Now it's arranged in ascending order. The moment you arrange these numbers in ascending order, the middle number will become the median. This is how you calculate median. Right? Mode: Mode is the most frequently occurring value in the data set. If I have 11234 five, which is a number that appears the maximum number of times in this data set, it is one. It's appearing twice, and "nonumber" is appearing twice here. Hence, that is called the mode. If I have only one mode, it is called unimodal. I can have a bimodal data set as well as a unimodal data set, I can have bimodal as well.112-2345 One is repeated twice; two are also repeated twice. No other number is repeated more than once. Hence, I have two modes, one and two. This is called a buy model. This is called a "bi-model" model," however you want to call it. I can also have a multimodal data set if there are a number of numbers that are repeating a number of times. All right, that is all about mode. Let us look at one more example. Three, four, five. In this scenario, the number that is repeated the maximum number of times is one. It's a repeated price. So hence I have one mode, which is called "one" in this case. So it is called "unimortal." All right, let us look into the various measures of dispersion. Now we have three measures of dispersion variance: standard deviation and range. Sigma square and the formula summation of x, which is each number minus the mean squared, and dividing it by the number of data points, are used to calculate variance. If it is a sample, the formula would change and the notations would change. It is a square. It is nothing but the summation of x minus x minus the square. You see small X's here because it's a sample. And here you see n minus one instead of n. This is a slight difference that you have to notice. If I take a square root ofvariance I would get standard deviation. Nothing else changes, but outliers have an impact on variance and standard deviations, just as they have on the minimum standard deviation. And in such cases, you go with the range. Range is nothing but the sum of the maximum and minimum values. If I have 1234 and five, the range would be five minus one, which is four. All right. Okay, here is a quick exercise for you to actually identify the mean, median, mode variance, and standard deviation range for these numbers. Yeah, you can either make use of Excel or the Minitab, or you can do a manual cancellation. It's left up to you. All right? Try it for your own understanding.

7. Internet Service Provider Case Study

Alright, here comes a case study. The good news is that we'll be moving away from theory and into practice. Now, here is a case study. We have two Internet service providers, and both of these have similar average call resolution times. The average time to resolve the calls is the same, despite the promised resolution time of 30 minutes. 30 minutes is what I promise the customers. I'll tell them or I told them that I would takea maximum of 30 minutes to resolve their issues over call. Now, when you have taken the average, you have seen that both of these Internet service providers on average have the same resolution time. Would you be correct in saying that they are equally good? Yes or no? The answer is no. You should not just stop at mean. "Mean" is the central tendency. He has discussed it in the previous slides. Not just that, you also have to look into the measures of dispersion variation to comment on which one is better. Would you like to consider variations in the resolution time as well? Yes. If yes, how would you measure the variation? Would you be looking at the range of the standard deviation? Which one do you think makes sense for you? Can we find a single measure for process performance that incorporates central tendency? The variation specification limits everything to a single shot. Can we do that? Answer: yes. A box plot is an example of that. All right, here is a case study. Two Internet service providers A and B answer approximately 1,000 technical calls a month. We recorded the call transaction time of 100 randomly selected sample calls per ISP customer who wanted issues to be resolved in 30 minutes. Now tell me which service provider is doing a good job. Is it A or B? In order to know this, let us open the minitab file and start working a little on the minitab. And, since I've already discarded, let us move on. Here is the data in minutes for Internet Service Provider A and Internet Service Provider minutesThe time taken in resolving the customer queries is provided here. All I need to do is go to "Start Basic Statistics" and then I want to display descriptive statistics. I click on that, and here is the pop-up window. I need to select Internet Service Provider One. Press the shift key and select Internet Service Provider B. Click on this button, select bothof these variables are selected. Now go to statistics and see what the various things are that you want to generate. I want the mean and the standard deviation. I want to see the variance. I want to see what a minimum value is. Maximum value. I want to see how many samples I have. What is the count of the data set? I want to see the first quarter, the third, and the median. Now I click on "Okay." Once I click on okay, let me click on okay once again here.And here are the descriptive statistics. So you need not worry about the navigation, etcetera. It's provided in the screenshots here. So it's extremely easy to navigate. Here is the count of output: We have picked up 100 samples, both for Internet Service Provider A and B, for sample analysis. Out of the 1000 calls I take in a month, 100 are a random sample. Look at the mean of A and B. It's approximately the same. So do you conclude that A and B are both doing a good job? No, we do not do so so early. We look into standard deviation as well. Oh my God! If I see the standard deviation, Internet Service Provider B is not doing a great job. There's a huge variation in the time taken to resolve the calls. The minimum time that Internet Service Provider B takes is five minutes, and the minimum time that Internet Service Provider A takes and resolves the connection is eleven minutes. Then you have Q 1, median Q 3, and the maximum value we will discuss about these things in the boxplot range is the maximum minus the minimum value if I look into the range at 16 and 24 here. As a result, the Internet Service Provider has a narrower range for resolving incidents or calls. Another topic we'll cover in the box plot is interquartile range. So hold on to your horses until ovider haLet us look at a graphical summary. Also, please allow me to return to the mini-tab file once more. Do not worry about the navigation. As I've told you, navigation paths are provided right in the screenshots. Do not worry about that. Understand the concepts first. Okay, in order to go back to the worksheet, I need to click on this Show Worksheet folder. I'm back on the worksheet now. All you need to do is go to start basic statistics, click on graphical summit, select Internet service provider one, press the shift key, select the other one, and click on the select option, then click on okay. And the magic box does the rest of the work for you. internet service providers A and B. We have the data set now. Okay, I have these two lined up, one beside another. Okay, look at the mean standard deviation variance the student scored. Also, we're not discussing this out of scope. How many points are there? 1000 data points—sorry, 100 data points here. Means, standard deviation, variance—either do this or try to look into that. By the way, this is called a boxplot, which we are going to discuss now. This is called a box plot. We have an outlier here. We'll discuss those things in just a minute. But just to give you a brief idea of how a graphical person looks, this is called a histogram. We'll understand that these bars are called a histogram. This graph that you see is called a probability distribution curve. Probability distribution function that provides this curveall right, so we will deep dive,as in, however progress, right? We'll try to understand, understanding, normal the valuesand all that confidence intervals and all that. But not now—this is just the introduction. So let me go back to the presentation.

8. Histogram, Barplot, Normal Distribution

Flip a coin 20 times? Why 20 times? Why not a hundred times? Right. So let me ask you this question. If I'm going to flip a coin once, what is the probability that I'll get ahead? You would obviously say it is 50%. If I toss a coin twice, what is the probability that I'll get ahead? Will you still go with 0.5? So are you 100% sure that if I flip a coin twice, I'm going to get the head once, and the next time I'm 100% going to get the tail? Can you say that with 100% with 100% confidenceIf I am flipping two coins, I might get zero heads, or I might get heads once, or I might get heads might get If I flip a coin three times, I might get zero heads, one head, two heads, or three heads. So the probability changes, and there might be multiple values that it might take. So if I flip a coin 20 times, record the number of hits that I'm getting each time. If I repeat steps one and two 500 times to represent 500 people, and then grab the results, I have flipped. And what is the probability of getting ahead? If I plotted it, this is what it would look like. And if I repeat this experiment a million, billion, trillion times, this will appear symmetrical. That is called a concept of the central limit theorem. I'll not discuss that in detail now. All right, let us look into another graphical technique, which is called a box plot. I can represent 100% of my data in a graphic format, which is called a box plot. Do not worry, we are going to do this box plot in Minitab as well, using the same Internet service provider case study. Just try to understand what a box plot looks like. What are the various options in that? The lowest position in a boxplot is called the minimum value. And these lines, which are extending here and here, are called as Whiskers.This line is called the lower quartile, or Q 1. The data from here until now would be 25%. The middle box is called the interquartile range. It contains approximately 50% of the data points. That box contains 50%. This is called the median, which we have already discussed. This is called upper quarter or Q three. From here until here, you'll get 75% of the data points, and this is called the maximum value, Q Three. Until maximum, you would have 25% of data. So 25% plus 75% would turn out to be 100%. 100% of the data can be represented diagrammatically using something called a box product. And if you have these kinds of dots or star marks somewhere outside the box plot, those are called outliers. So this is how you navigate the Mini Tab. Whatever the box plot, I'll try to do this for you b. WhateveHow do I go back to the worksheet? I just click on the symbol Show Worksheets folder. I go back to the worksheet. Now, how do I navigate and go to the Box Plot? Simple. Go to the graph and box plot. I have two y's, or two entries here, Internet Service Provider A and B. So let's select two and click on "okay," then I select Internet Service Provider A. Press the Shift key, select Internet Service Provider, and click on "Job Done ask you this question. If I'm going to flip a coin once, what is the probability that I'll get ahead? You would obviously say it is 50%. If I toss a coin twice, what is the probability that I'll get ahead? Will you still go with 0.5? So are you 100% sure that if I flip a coin twice, I'm going to get the head once, and the next time I'm 100% going to get the tail? Can you say that with 100% confidence? No. Right. If I am flipping two coins, I might get zero heads, or I might get heads once, or I might get heads twice. What? If I flip a coin three times, I might get zero heads, one head, two heads, or three heads. So the probability changes, and there might be multiple values that it might take. So if I flip a coin 20 times, record the number of hits that I'm getting each time. If I repeat steps one and two 500 times to represent 500 people, and then grab the results, I have flipped. And what is the probability of getting ahead? If I plotted it, this is what it would look like. And if I do this experiment a million times, a billion times, a trillion times, then this would look symmetrical. That is called a concept of the central limit theorem. I'll not discuss that in detail now. All right, let us look into another graphical technique, which is called a box plot. I can represent 100% of my data in a graphic format, which is called a box plot. Do not worry, we are going to do this box plot in Minitab as well, using the same Internet service provider case study. Just try to understand what a box plot looks like. What are the various options in that? The lowest position in a boxplot is called the minimum value. And these lines, which are extending here and here, are called whiskers. This line is called the lower quartile, or Q 1. The data from here until now would be 25%. The middle box is called the interquartile range. It contains approximately 50% of the data points. That box contains 50%. This is called the median, which we have already discussed. This is called upper quarter or Q three. From here until here, you'll get 75% of the data points, and this is called the maximum value, Q Three. Until maximum, you would have 25% of data. So 25% plus 75% would turn out to be 100%. 100% of the data can be represented diagrammatically using something called a box product. And if you have these kinds of dots or star marks somewhere outside the box plot, those are called outliers. So this is how you navigate the Mini Tab. Whatever the box plot, I'll try to do this for you guys. Okay? How do I go back to the worksheet? I just click on the symbol Show Worksheets folder. I go back to the worksheet. Now, how do I navigate and go to the Box Plot? Simple. Go to the graph and box plot. I have two y's, or two entries here, Internet Service Provider A and B. So let's select two and click on "okay," then I select Internet Service Provider A. Press the Shift key, select Internet Service Provider, and click on "Job Done." Okay, magic. Right here is a box. This is a box plot for Internet Service Provider A. This is for B. And this is an outlier star.This is the bare minimum. This is called Q 1. From here until here, you will have 25% of the data. This box is called an interquartile range," which contains 50% of the data. This line is a median. The stop is called as Q three.There will be 75% of the data points from here until the whisker end. And this highest point is called the maximum point." Same goes with Internet Service Provider A as well. This is the star. Let us see whether we can select that item. Yes, that's the option. I want you to carefully observe this. When I highlight the star, it shows me that row 90 is a culprit here. Return to the data set and investigate what this row 90 of Internet Service Provider Be means. I clicked on this to go back and see what row 90 means. and row 90, which is an outlier. Clicking on this row returns 90 of Internet Service Provider B if I select it. Internet Service Provider B is in this column. Let me see. Oh, here it is. There's a small, right-angled point. Someone has taken five minutes in order to resolve a customer issue. And none of the other points show that. Most of the other points are in 2019 minutes, 18 minutes, eleven minutes, and so forth. That's an exceptional point. Hence, it is showing as an outlier. All right, let me go back to the presentation and let us look into the other stuff. Okay? Normal distribution is extremely beautiful. Like the curve shows, you're right: it's approximately symmetrical. So you can represent a normal distribution, which is characterised by the mean, mu, and standard deviation. Look at this. MU is equal to zero. standard deviation is equal to one. If you give those two this blue graphrepresents this mu is equal to zero. Standard deviation is equal to zero five. That's represented in this graph. Now look at the difference if the mean remains ro. StandAnd if the standard deviation decreases, your normal curve becomes thin and your height increases. Let us see what happens if the mean remains decent and the standard deviation increases. If the mean remains the same and the standard deviation increases, then it's represented using this green graph. This one dark green graph heightens in comparison to the blue. And also, it gets wider. All right, so if the mean is the same and the standard deviation increases or decreases, what is going to happen is explained so, it gets wNow let us see what would happen if the standard deviation remained the same. That is, the variation remains the same, but the mu changes from zero to minus one. It's represented with this orange line here. So there is a shift. If it is negative, this particular graph is moving towards the left. If the mean is positive, it's moving towards the right. It's represented in the graph. This is a small explanation. So you can characterise each and every normal distribution curve using two values: the new mean, the population mean, and the standard deviation, the population standard deviation. It is characterised by a bell curve. If you see the curve, it looks like a bell, right? And it has the following properties. 68.26% of values lie within plus or minus one standard deviation from the mean. If this is the standard, If this is plus one and minus one, the number of data points that satisfy the customer requirements would be 68.26 if it's operating at plus or minus. If the process operates at plus or minus two sigma standard deviation, then approximately 95.44% of the data points meet the customer requirements or meet the specification limits. If you look at plus or minus three sigma, it's 99.73 plus or minus three sigma. Most people say this, or they have a wrong way of interpreting this. They say one standard deviation, two, and three on one side, and then on the other, they also have three standard deviations. All these three sum up to six standard deviations, and that is six sigma. No, my dear friends, you will go wrong in this interpretation. If you interpret it in this manner. Six sigma means there have to be six standard deviations that fit into the range on one side of the specification limit. I have six standard deviations, and this is the formula. 99.99% of the requirements of the datapoints or of the products need the specification. That is how you will have to interpret this. or it can be on the other side. Also, if there are six standard deviations from the other side of the specification limit, it is called the six-sigma process. Yes, think about the same example. The upper specification limit of an ICC cricket ball is 229, and the lower specification limit of an ICC cricket ball is 224. Yeah, this is what you would get.

9. Probability Distribution Plot

We know the histogram concept. We know if I plot, it's going to follow some distribution, which is called a probability distribution plot. So let me switch back to Minitab and explain this concept as well. All right, don't worry about the navigation; it's provided there. We just need to go to a graph of probability distributions. Plot. Okay, I'm on. This worksheet. To plot the probability distribution, I need to go to the library. Plot? I want to view the probability, and I want to do this for both of the service providers, Internet Service Provider A and Internet Service Provider. But I need to know the mean and standard deviation for both Internet Service Provider A and B. Already, we have done that exercise. Let me go here. This small icon here is going to tell you the various things that you have done in the session. Okay, it brings me back to the first exercise that we have performed in doing descriptive statistics. So now let me go to the probability distribution plot. I'd like to see the probability and see how likely it is that my Internet Service Provider will take longer than 30 minutes to resolve my calls. because 30 minutes is the customer expectation. I call customer care for any issue with the Internet, I call the customer care.They have to resolve it within 30 minutes. That's my goal. Now I want to check what the probability is that Internet Service Provider A would exceed 30 minutes in resolving my issues based on the historical data. I also want to check the probability that Internet Service Provider B will exceed 30 minutes in resolving my issue. So let me click on Okay, we know that it was following normal distribution. You might ask me, "How do you know that it was following normal distribution?" We cancel this. Let me go to the graphical summary. Now comes a small concept called Anderson Darling Normality Test. And if the P value is greater than 0.5, it's greater than 0.5. If it is greater than 0.5, it follows a normal distribution. It's also visible when you look at the graph. So just understand that we will do a deep dive into this, both in how we move forward and in how we progress in the program. Let me see whether Internet Service Provider BE is also following a normal distribution. If I look at the curve, it seems to follow the normal distribution. But let me look into ad testing. Anderson, darling. The p value for the normality test is seven. Is it greater than 0.5? Yes, it is greater than zero five.As a result, you conclude that the data from Internet Service Providers A and B are normally distributed. Let me click on descriptive statistics. Let me go to the probability distribution plot. View the probability and click on "Okay," so we know that it's following a normal distribution. There are other distributions also available, but for us, we know that it's following the normal distribution. What is the meaning of "Internet Service Provider A"? It's given here, meaning for Internet Service Provider A, it is 19.48. And what is the standard deviation for Internet Service Provider A? The standard deviation is 3.69 68 nine.If I click on "okay," look at this. It says that there is a 0.5% probability that Internet Service Provider A would exceed 30 minutes. Yeah, I purposefully did this. Look at hat InternFor those of you who are sleeping, wake up. For those of you who were awake, you caught this, right? So if I want to go back to the previous screen on which I was working, I need to click on this option. Edit the last dialogue box. I come back here. I go to the shadow region. I want to find out the probability that Service Provider A exceeds 30 minutes. Now click on "Okay." Now it says that there is a probability of 0 points 17 percent that your Internet Service Provider will exceed 30 minutes in resolving your issues. That's for Internet Service Providers; look at this. 0.5, so very minuscule. Now let me go back to the descriptive statistics that we have done. Now I'll go back to the graph-probability distribution plot and view probability. Click on "Okay." Now I'll do the same exercise for Internet Service Provider B. What is the meaning here? The mean is 19.46. What is the standard deviation for Internet Service Provider B? Five. Five. I do not click on okay yet. Don't repeat the mistake. Go to shadow region, click on X value. I want to check the probability of Internet Service Provider B exceeding 30 minutes and resolving my issues. I click on "Okay." It says Internet Service Provider B has a probability of 0.0% to 6% of exceeding 30 minutes in resolving your issues. This clearly says Internet Service Provider A has done a good job and this is for B. Alright friends, let us go back to the presentation. Do not worry about the navigation. It's clear. Little is mentioned over there. Look at this. What is Six Sigma Performance? We already discussed this. If you have a Six Sigma process and you feel that process should operate at Six Sigma, that means you should be able to fit in six standard deviations. six standard deviations from the mean. My bad. Let me redraw that. I'm bad at drawing, by the way. From here until here, you need to fit in six standard deviations. And if you can fit in six standard deviations, then you can claim that you're operating at six-sigma Sigma process.Think about boxing competitions, right? Freud Mayweather has never lost a single match. What makes him so strong? And if you say that I want to go and have a match against Floyd Mayweather, no one is going to entertain titions,because they're going to test you. How much time can you withstand if I throw punches as hard as Floyd Mayweather? Right? How many standard deviations, or punches a boxer can take while still meeting the specification limits or remaining in the ring without being knocked out, That is called the standard deviation and the six sigma process, right? So you need to just fit in six standard deviations. Assume that the variation in the process is high. If the variation is high, the standard deviation would be more. Suppose this is my specified limit. Specification limits. By the way, my dear friends, it will not change. The customer has told me that the upper specification limit should be 229, The lower specification limit for an ICC Cricket Ball's circumference should be 224. Those will not move. If your standard deviation is small, say, two standard deviations, then you can fit in only two standard deviations. And if you can fit in only two standard deviations from the mean to the specification limit, your process is called following two sigma," not six sigma. and only if you can reduce the width of the standard deviation. You can fit six standard deviations into that. Let me ask you one question even before we move on. Does the aid lines industry operate at what sigma level, or does the pharmaceutical industry operate at six sigma? Six sigma means 3.45 per million opportunities. Say there are a million flights that are taking off or landing. By the way, a million flights would take off on land in a week, including domestic, international, and helicopters, is that correct? Within a week, a million people would be in contact. within a week. Are you hearing that there are three crashes out of four crashes? No, they do not operate at six-sigma sigma level.Airlines, your nuclear, missile, space launching, healthcare, they operate at a sigma levelwhich is much higher than six sigma. If you claim it is eight sigma, a few claim it is nine, and a few claim twelve. But to be honest, it is much higher than six sigma. All right, now you know the differencebetween standard deviation and sigma level. The z value, or standard deviation, is represented by this Greek letter as the sigma level. There is one more thing that I want to mention even before we move on. All population representation, including new, is intended for the population. Sigma square is a variance of population. Sigma is the standard deviation of a population. All these are Greek letters. The population of a sample is represented using xbar, the variance of a sample using s squared, and the standard deviation of a sample using s. So that's how you differentiate. Also, we know that the formula changes for variance and standard deviation when it comes to population versus sample. We also know that the notations change from "new" to "sample" in the formula I used to calculate. All right, this is a simple representation of sigma level. If your process is operating at a two-sigma level, there will be so many defects per he formula changeIf you're operating at a four-sigma level, 6210 Defixis is what you would see in your process. If you're operating at a six-sigma level, then you would see that there are 3.40 defects per million opportunities, right? Moving from two sigma to three sigma, three to four, four to five, and five to six is a peculiar task. To be safe, if you're doing a consulting engagement for a client and they're at three sigma, don't promise to take their process from three to six sigma by implementing a six sigma project. not possible at all. All you can do is move from three to four sigma, then from four to 4.5, then to five, and finally to six. The higher the sigma that you want to attain, the more difficult it will be for you to implement the hree sigma, By the way, st stands for short term.We will discuss short-term and long-term fees when we discuss the major fees. Until then, hold on to your do is move mIf you operate at a 3.8 sigma level, you will see 99% positive results. But if you're operating at six-sigma levels, you'll see 99.96% good things. That's the difference. Though, in percentage terms, you might think there isn't much of a difference between 6210 and 3.46. This is called a breakthrough methodology. All right, now let us differentiate between this and that. We have already done that on the previous slide. But let us try to understand once again that as the variation or the standard deviation reduces, so do the defects. Defects also reduced significantly, as in how the variation reduced and the defects reduced, so your sigma level went up, which is your six sigma. Alternatively, if you want to attend six sigma training, your variation and defects should decrease. Going back to the definition of six sigma, which we have discussed in the first few slides, six sigma is all about reducing variation and reducing defects, right? Okay. There are few assumptions that specification limitsof the customer requirements, goals do notchange and process average remains constant. Those are the two assumptions. This is by far the most important equation in Six Sigma. Or, I would say, this is by far the most beautiful equation that I've seen. Any output y is a function of inputs and is dependent on a few inputs. The weight of a person is dependent on calories consumed and salary drawn, which is output, which depends on a number of certifications that I possess. Years of experience that I possess and a graduation degree that I possess Right. If I say I'm a six sigma greenbelt, I'll probably get some money. If I said I was a Six Sigma black belt, obviously I would get a higher salary. If I mention that I'm a Six Sigma mass black belt, my salary will obviously rise. So any output depends on the function of its inputs. The mileage of a car is determined by its horsepower, cubic capacity, suspension, air pressure, the number of passengers it can carry, and the variant—is it a petrol or diesel vehicle? Right. All those are going to define my mileage. As a result, y equals f of x. To get results, we should focus on our behaviour on y or x; that is the question. Now, to answer that, let us answer this. Is it feasible to eliminate the inspection of XS if they are controlled? If I take care of my inputs, will the output be taken care of? Absolutely yes. Try to improve your inputs. Your output is automatically taken care of. That's the law of nature. By the way, here are the various names for your output variable. It's also called dependent because it is dependent on your inputs. It's also called an output effect, symptom monitor, or response variable. It's going to respond to the inputs. X, which is your input, is also called an independent variable, cost, problem, control factor, and so on and so forth. You need to understand these different terminologiesbecause different mathematical, statistical six sigma booksuse different terminology, different terminology. So you need to be aware of all that. Alright, a quick summary of whatever we have discussed until now is as follows: We discussed six-sigma history and how it evolved. We also discussed the basics of six sigma methodologies, including DMAIC, the Mac, and the form of six sigma designed by DMA DV. We discussed elementary statistics. We have discussed measures of central tendency and measures of dispersion, right? The mean median mode is discussed. We discussed about variantstandard deviation and range. We looked at a few of the options available on Minitab, and we worked on an Internet service provider case study. Yeah, we have also looked at the histogram and what that means. We have also looked into box plot,the various options available in box plot. We looked at quartile 1, the minimum value, the interquartile range, quartile 3, the maximum value, and also the outlier box spot. We discussed probability distribution, and normal distribution was something on which we spent some additional time on.We also try to look into the differences between what a sigma means and what a sigma level means. Lower the sigma, lower the defects, higher the sigma level, lower the sigma, lower the defects, higher the sigma level. And finally, we looked into one of the most beautiful and important equations. That is, any output Y is dependent on one input or multiple inputs. With this, I stop here and look into subsequent sections in order to understand what happens in a defined phase, what happens in the measure and analyze phases, and how to improve fees and control fees. All right, I'm extremely happy to have recorded the session for you all. I hope you found this extremely useful. Thank you. and let us look into this programme a little further. See you.

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