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<v Speaker 1>Welcome to the deep dive. You know, when most people

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<v Speaker 1>hear machine learning or maybe AI, I think the first

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<v Speaker 1>thing that comes to mind is the code.

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<v Speaker 2>Right, Oh, absolutely, Python, scripts, neural nets, all that complex

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<v Speaker 2>engineering stuff. That's the flashy part.

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<v Speaker 1>Yeah, the engine, It is the engine. Yeah.

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<v Speaker 2>But what our source material for today really emphasizes, and

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<v Speaker 2>it's looking specifically at the prerequisites for even building those engines,

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<v Speaker 2>is that the real foundation. It isn't the code, ok,

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<v Speaker 2>it's math specifically, it's statistics. You could almost call it

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<v Speaker 2>a preliminary requirement.

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<v Speaker 1>Right. So that's our mission today. Then we're aiming to

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<v Speaker 1>give you a bit of an intellectual shortcut here. We

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<v Speaker 1>want to pull out the essential statistical concepts that the

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<v Speaker 1>core of vocabulary and the toolkit you need for exploring data,

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<v Speaker 1>cleaning it up, getting ready for predictive modeling.

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<v Speaker 2>Basically saving you the trouble of reading the whole textbook page.

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<v Speaker 1>By page exactly. This is about getting that statistical fluency

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<v Speaker 1>you need before you even think about training.

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<v Speaker 2>A model, and it's not just about passing some exam.

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<v Speaker 2>You genuinely need these concepts because well, every single step

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<v Speaker 2>in an mL pipeline from the moment you get the

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<v Speaker 2>data to evaluating how well your model did. It's fundamentally

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<v Speaker 2>a statistical operation.

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<v Speaker 1>Okay, so where do we start. I guess right at

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<v Speaker 1>the beginning, recognizing what kind of data you're even dealing with.

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<v Speaker 2>That's the spot the sources remind us that data collection

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<v Speaker 2>isn't just you know, chaos. It's usually driven by trying

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<v Speaker 2>to answer some real world question.

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<v Speaker 1>Like market research before you launch a product, maybe.

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<v Speaker 2>Exactly is this product feasible? Who are we trying to

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<v Speaker 2>reach that kind of thing?

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<v Speaker 1>And the answers we get the actual numbers we collect

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<v Speaker 1>in store.

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<v Speaker 2>Those are grouped into what statisticians call random variables. They're

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<v Speaker 2>the numerical backbone of whatever research you're doing.

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<v Speaker 1>Okay, random variables, So how do we bring some order

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<v Speaker 1>to that? How do we structure them?

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<v Speaker 2>Well, we mainly split them based on what they can

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<v Speaker 2>actually measure. First up, you've got discrete random variables.

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<v Speaker 1>Discrete meaning separate.

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<v Speaker 2>Yeah, I think fixed counts. They have to be whole numbers.

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<v Speaker 2>It can't be like counting how many people clicked on

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<v Speaker 2>an ad or the number of gold medals a country

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<v Speaker 2>one in the Olympics. Not it fixed counts, Definite fixed counts.

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<v Speaker 1>So what's the other kind the stuff that isn't fixed counts?

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<v Speaker 2>That would be your continuous random variable. This one stores

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<v Speaker 2>values that can be decimals or floats, and theoretically, at

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<v Speaker 2>least you could measure them with infinite precision.

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<v Speaker 1>Like height or weight.

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<v Speaker 2>Perfect examples height, weight, temperature. You can always, in theory,

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<v Speaker 2>add another decimal place to make the measurement finer.

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<v Speaker 1>Okay, that makes sense for numbers, But what if the

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<v Speaker 1>data isn't a number at all, Like if it's just

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<v Speaker 1>a label someone's city or maybe their preferred brand.

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<v Speaker 2>Ah, good question. Then you're working with categorical variables. And

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<v Speaker 2>this is where we need another layer of distinction, because

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<v Speaker 2>how an mL algorithm handles these depends a lot on

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<v Speaker 2>whether the categories have some kind of internal meaning or order.

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<v Speaker 1>Wait, internal meaning? Why does that matter? Isn't red just

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<v Speaker 1>red to a computer?

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<v Speaker 2>It matters quite a bit, actually, mostly because it impacts

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<v Speaker 2>how you encode that data before feeding it to a model.

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<v Speaker 2>If the categories have absolutely no inherent rank or order,

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<v Speaker 2>we call them nominal variables. Okay, think gender like male female,

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<v Speaker 2>or maybe types of fruit apple, banana, orange. You can't

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<v Speaker 2>really rank one above the other. Logically, they're just distinct groups.

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<v Speaker 1>Right, distinct groups makes sense, But what if they can

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<v Speaker 1>be ranked and it's.

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<v Speaker 2>An ordinal variable. Think about say a customer satisfaction rating low, medium, high.

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<v Speaker 1>Ah, Okay, there's a clear hierarchy.

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<v Speaker 2>There exactly, And knowing this difference is key before you

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<v Speaker 2>start your future engineering phenomenal variables. The algorithm often needs

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<v Speaker 2>to treat each category as totally separate, maybe using something

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<v Speaker 2>called one hot encoding. But for ordinal variables you might

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<v Speaker 2>be able to use encoding methods that preserve that ranking,

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<v Speaker 2>which can sometimes make the model simpler or even more accurate.

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<v Speaker 2>So yeah, knowing this distinction is pretty fundamental.

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<v Speaker 1>All right, So we figure fur out what kind of

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<v Speaker 1>variables we have. What's the immediate next step? Usually it's

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<v Speaker 1>descriptive statistics, right, trying to summarize potentially huge data sets.

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<v Speaker 2>Yes, exactly. We're moving from just defining things to actually

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<v Speaker 2>starting to tell the story hidden the data. The first

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<v Speaker 2>step is usually summarizing it, focusing on its center and

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<v Speaker 2>it's spread.

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<v Speaker 1>Okay, center and spread. Let's start with the center. Measures

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<v Speaker 1>of central tendency is that the term that's the one and.

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<v Speaker 2>The big three here are the mean the median and

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<v Speaker 2>the mode.

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<v Speaker 1>Everyone knows the mean the average, Right, add them all up,

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<v Speaker 1>divide by how many there are. Seems simple, But what's

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<v Speaker 1>the specific mL insight? Why is it so important?

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<v Speaker 2>Well, mathematically, the mean is the center of balance for

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<v Speaker 2>your data. But what's really interesting is how it connects

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<v Speaker 2>directly to prediction. How So, when you build, say a

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<v Speaker 2>simple linear regression model, what you're essentially doing is trying

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<v Speaker 2>to draw a line that minimizes the square distance between

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<v Speaker 2>that line and all your data points. Yeah, the mean

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<v Speaker 2>turns out to be the single value that inherent only

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<v Speaker 2>minimizes that scored error.

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<v Speaker 1>Huh. So it's like the best guess if you knew

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<v Speaker 1>nothing else.

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<v Speaker 2>It's the optimal point prediction if you had zero other information. Yes,

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<v Speaker 2>it's a point of minimum error.

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<v Speaker 1>Okay, but the mean has that famous weakness, right, the

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<v Speaker 1>outlier problem. Like if your averaging salary is in a

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<v Speaker 1>small startup and suddenly the CEO's twenty million dollars salary

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<v Speaker 1>gets added.

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<v Speaker 2>In exactly that one massive outlier just yanks the average

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<v Speaker 2>way way up, making it not very representative of the

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<v Speaker 2>typical employee.

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<v Speaker 1>So that's where the medium comes in.

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<v Speaker 2>Precisely, The median is the exact middle value when you

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<v Speaker 2>sort your data from smallest to largest. Fifty percent of

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<v Speaker 2>the data is below it, fifty percent is above it.

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<v Speaker 1>And because it only cares about the middle position.

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<v Speaker 2>It's incredibly robust to those extreme outliers. That twenty million

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<v Speaker 2>dollars salary doesn't really affect the median much, if at all.

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<v Speaker 1>And if you have an even number of data points,

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<v Speaker 1>no single middle value.

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<v Speaker 2>Simple you just take the average of the two middle values.

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<v Speaker 2>Still gives you that robust central point.

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<v Speaker 1>Okay, so mean is air minimizing, but sensitive to outliers,

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<v Speaker 1>meeting is robust. What about the third one, the mode?

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<v Speaker 2>The mode is even simpler. It's just the value that

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<v Speaker 2>shows up most often in your data set, most frequent yep.

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<v Speaker 2>It's typically most useful for categorical data, finding the most

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<v Speaker 2>popular choice or the most common group.

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<v Speaker 1>And he quirks with the mode.

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<v Speaker 2>Couple interesting ones. It's the only measure of center that

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<v Speaker 2>might not actually be present in your data, which sounds

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<v Speaker 2>weird but can happen. And you can also have more

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<v Speaker 2>than one mode, like bimodal exactly by moodal if there

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<v Speaker 2>are two peaks, or even multimodal that can be a

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<v Speaker 2>clue that your data might actually be composed of a

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<v Speaker 2>couple of different underlying groups or clusters.

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<v Speaker 1>Okay, so we found the center using mean, median or mode.

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<v Speaker 1>But you said center alone isn't enough. Two data sets

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<v Speaker 1>could have the same mean but look totally different.

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<v Speaker 2>Right. Imagine one data set clustered tightly around the mean

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<v Speaker 2>and another spread way out, same mean, very different story.

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<v Speaker 2>That's why we need measures of disperge or spread, and

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<v Speaker 2>the main ones are variance in standard deviation STY.

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<v Speaker 1>Okay, variance and STY. They both measure spread, right, how

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<v Speaker 1>far data points tend to be from the center, usually

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<v Speaker 1>the mean.

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<v Speaker 2>That's the core idea. A high value for either variants

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<v Speaker 2>or SD means the data is really spread out, dispersed widely.

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<v Speaker 2>A small value means everything's huddled close to the mean.

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<v Speaker 1>So if they measure the same basic thing, why do

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<v Speaker 1>we need both? What's the practical difference, especially thinking about

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<v Speaker 1>machine learning?

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<v Speaker 2>Okay, so mathematically, the standard deviation is just the square

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<v Speaker 2>root of the variance. The absolute key difference is the

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<v Speaker 2>units units. Yeah, variance is calculated using square differences, so

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<v Speaker 2>it's units are the square of the original data's units.

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<v Speaker 2>If you measure at height in meters, the variance is

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<v Speaker 2>in meters squared, which is kind of awkward to interpret directly.

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<v Speaker 1>Not very intuitive.

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<v Speaker 2>But the standard deviation, because it's the square root, is

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<v Speaker 2>back in the original units. So if your height data

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<v Speaker 2>is in meters, the SD is also in meters.

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<v Speaker 1>Ah. Okay, so s D is easier to compare directly

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<v Speaker 1>to the mean.

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<v Speaker 2>Much easier. It makes SD far better for interpretation, for reporting,

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<v Speaker 2>and really crucially for something called feature scaling or normalization

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<v Speaker 2>in mL.

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<v Speaker 1>Why future scaling.

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<v Speaker 2>Well, often in mL you have features measured on totally

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<v Speaker 2>different scales, maybe aging years, income in thousands of dollars,

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<v Speaker 2>heightened centimeters. Models can sometimes struggle with that or give

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<v Speaker 2>too much weight to features with larger numerical values.

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<v Speaker 1>So you need to put them on a level playing

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<v Speaker 1>field exactly.

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<v Speaker 2>You often rescale features so they have a mean of

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<v Speaker 2>zero and a standard deviation of one, And standard deviation

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<v Speaker 2>is the metric you use to do that rescaling properly.

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<v Speaker 2>It's fundamental for pre processing data for many algorithms.

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<v Speaker 1>Okay, we've gone from defining data types to summarizing them

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<v Speaker 1>with center and spread. Now how do we pivot towards

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<v Speaker 1>using this data for prediction. That feels like the next

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<v Speaker 1>logical step.

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<v Speaker 2>It is, and that pivot really starts by defining a

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<v Speaker 2>potential cause and effect relationship. This is where we introduce

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<v Speaker 2>the concepts of dependent and independent.

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<v Speaker 1>Variable right setting up the experiment.

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<v Speaker 2>Essentially, pretty much, we're defining our modeling goal. What factor

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<v Speaker 2>are we changing or observing the independent variable, and what

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<v Speaker 2>outcome are we measuring the effect on the dependent variable.

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<v Speaker 1>So the independent variable is the input, the thing we control,

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<v Speaker 1>or the factor we think is causing a change.

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<v Speaker 2>Exactly like in a drug trial, the dosage level would

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<v Speaker 2>be the independent variable. Or using an example from the source,

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<v Speaker 2>maybe the type of pitch a pitcher throws to a batter.

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<v Speaker 2>That's the input being.

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<v Speaker 1>Varied, and the dependent variable is the output the result

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<v Speaker 1>What happens because of the independent variable.

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<v Speaker 2>Yes, it's the variable being tested or measured that responds

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<v Speaker 2>to the changes. In that baseball example, the batter's performance,

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<v Speaker 2>did they hit it how well? That's the dependent variable.

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<v Speaker 2>Its value depends on the pitch type.

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<v Speaker 1>And getting these two defined correctly seems absolutely critical. It's

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<v Speaker 1>basically framing the entire problem you want your mL model

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<v Speaker 1>to solve.

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<v Speaker 2>It is you're specifying the relationship you intend to model

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<v Speaker 2>and predict.

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<v Speaker 1>Now, underpinning all all of this statistical analysis, all these

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<v Speaker 1>measurements and relationships, there's a really core principle that gives

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<v Speaker 1>us confidence in the results, right, the law of large

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<v Speaker 1>numbers LLLN.

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<v Speaker 2>Ah. Yes, the LLN. It's absolutely fundamental. It's kind of

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<v Speaker 2>the bedrock that makes statistics work reliably.

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<v Speaker 1>So what is its state? In simple terms, it.

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<v Speaker 2>Basically says that if you repeat the same experiment over

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<v Speaker 2>and over and over again a huge number of times,

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<v Speaker 2>the average of the results you get will get closer

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<v Speaker 2>and closer to the true expected theoretical value.

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<v Speaker 1>Like flipping a coin.

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<v Speaker 2>Perfect example, flip a coin just ten times, you might

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<v Speaker 2>easily get say seven heads and three tails. That's pretty

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<v Speaker 2>far from the expected fifty to fifty, right, But flip

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<v Speaker 2>that same coin a million times or ten million times,

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<v Speaker 2>the ratio of heads to tails is going to get

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<v Speaker 2>incredibly close to exactly one to one. It converges on

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<v Speaker 2>the true probability.

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<v Speaker 1>And it's that convergence that lets us trust statistical methods exactly.

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<v Speaker 2>It validates the whole idea of using probabilities and statistics

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<v Speaker 2>derived from experiments or samples to stand underlying truths. It

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<v Speaker 2>allows us to have confidence in probabilistic models.

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<v Speaker 1>So the LN gives us the confidence then to take

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<v Speaker 1>results we see in a smaller sample of data and

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<v Speaker 1>make reasonable conclusions about the entire population it came from,

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<v Speaker 1>which sounds like statistical inference.

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<v Speaker 2>That's precisely what statistical inference is about, and it leads

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<v Speaker 2>directly to the main framework we use for making those decisions.

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<v Speaker 2>Hypothesis testing.

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<v Speaker 1>Okay, hypothesis testing. This is where we formally test an

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<v Speaker 1>idea using the data.

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<v Speaker 2>Yes, it's the structured process where we use the summary

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<v Speaker 2>statistics we calculated combined with our understanding of probability in

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<v Speaker 2>the LLN to draw conclusions about a whole population based

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<v Speaker 2>only on evidence from a sample.

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<v Speaker 1>And it usually involves setting up two competing ideas beforehand.

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<v Speaker 2>Correct you have a kind of statistical showdown. The main

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<v Speaker 2>goal is to see if there's enough evidence in your

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<v Speaker 2>sample data to reject the null hypothesis.

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<v Speaker 1>The null hypothesis being the default skeptical position.

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<v Speaker 2>Always it's the statement of no effect, no difference, or

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<v Speaker 2>no relation. For example, this new drug has no effect

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<v Speaker 2>on recovery time compared to the place ebo. It's the

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<v Speaker 2>status quo assumption, and we test that against against the

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<v Speaker 2>alternative hypothesis. This is the statement that contradicts the null.

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<v Speaker 2>It's what you, as the researcher, might actually suspect or

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<v Speaker 2>hope to prove, like, no, this new drug does reduce

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<v Speaker 2>recovery time.

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<v Speaker 1>So the whole process is about gathering enough statistical evidence

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<v Speaker 1>to confidently say, Okay, we can reject the no effect

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<v Speaker 1>idea in favor of the there is an.

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<v Speaker 2>Effect idea precisely, and that level of statistical confidence, often

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<v Speaker 2>expressed as a P value or a confidence interval, is

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<v Speaker 2>what determines whether you feel justified in acting on your

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<v Speaker 2>findings or making a claim about the population.

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<v Speaker 1>All right, let's pull this together. We've walked through quite

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<v Speaker 1>a statistical toolkit, understanding the different types of variables you encounter.

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<v Speaker 2>Discrete, continuous, nominal, ordinal.

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<v Speaker 1>Yeah, then summarizing them with measures of center like the

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<v Speaker 1>mean and median, understanding spread with standard deviation especially ysds

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<v Speaker 1>full practically.

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<v Speaker 2>Right, those units matter for comparison and scaling.

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<v Speaker 1>Then we moved into setting up predictions by defining dependent

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<v Speaker 1>and independent variables, and finally, the framework for making decisions

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<v Speaker 1>based on sample data hypothesis testing built on the confidence

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<v Speaker 1>given by the law of large numbers.

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<v Speaker 2>It really does form the essential foundation. You can see

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<v Speaker 2>how these concepts are well mandatory before you jump into

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<v Speaker 2>the more complex mL algorithms.

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<v Speaker 1>They really are the entry point for any serious study

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<v Speaker 1>or application.

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<v Speaker 2>But here's a final thought, something that connects back to

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<v Speaker 2>that law of large numbers. The LN guarantees convergence. It

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<v Speaker 2>gives us certainty, but only over a massive number of trials.

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<v Speaker 2>A million coin flips.

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<v Speaker 1>Right, requires huge scale exactly.

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<v Speaker 2>But in the real world, doing market analysis, building a

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<v Speaker 2>product prototype, maybe even running a clinical trial, we almost

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<v Speaker 2>never have a million data points. We work with samples,

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<v Speaker 2>sometimes relatively small samples because collecting data is expensive or

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<v Speaker 2>time consuming.

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<v Speaker 1>So the certainty we get is an absolute. It's usually probabilistic,

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<v Speaker 1>like saying we're ninety five percent confident or maybe ninety

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<v Speaker 1>nine percent confident.

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<v Speaker 2>Right, which leads to the provocative question. If the law

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<v Speaker 2>of large numbers only guarantees truth over immense scale, how

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<v Speaker 2>often are our everyday decisions, maybe in business, launching a

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<v Speaker 2>new feature, or even interpreting a political poll, actually based

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<v Speaker 2>on what could be called the fallacy of small.

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<v Speaker 1>Numbers, meaning we're drawing conclusions from samples that might be

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<v Speaker 1>too small to really trust the LLNS guarantee potentially.

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<v Speaker 2>So the question for you, the listener, is what level

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<v Speaker 2>of statistical certainty that ninety five percent, that ninety nine

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<v Speaker 2>percent are you willing to accept, Especially when you're moving

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<v Speaker 2>from analyzing a potentially small, expensive sample to making a

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<v Speaker 2>big assumption about the entire population, an assumption that could

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<v Speaker 2>have major consequences, maybe cost millions.

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<v Speaker 1>How much uncertainty can you live with?

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<v Speaker 2>What's your threshold for risk framed in that statistical confidence?

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<v Speaker 1>Definitely something to think about. A great place to leave

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<v Speaker 1>it for the steep dive. Thanks for joining us,