Intro to Stats: Videos & Practice Problems

Statistics involves collecting and analyzing data to make informed decisions about populations and samples. A population includes all members of a group, while a sample is a subset of that population. Data can be qualitative (attributes or labels) or quantitative (numerical measurements), which further divides into discrete (countable values) and continuous (measurable values). Understanding these concepts is crucial for effective data analysis and interpretation.

Parameters vs. Statistics

Hello, everyone, and welcome to the course. Because it's the very first video, I don't want to get into anything super technical or complicated. Instead, I want to just focus on some basic definitions for what statistics is all about, as well as some keywords and definitions you'll be hearing a lot throughout the course. Then we'll do some examples together. So let's get started.

So what is statistics all about? It's basically just a branch of science in which you're going to collect and then do a bunch of stuff with data in order to learn more about a group of people or companies or things, something like that, in order to make informed decisions. So you collect data, and then you just do a bunch of stuff with it. Now, I know that that word data sounds kind of scary because you're picturing these spreadsheets with a bunch of numbers, rows, and columns, and things like that. But it's not really that complicated because when we use the word data, all it means is that we're collecting information.

And, yes, sometimes we go out and count or measure that information. For example, I can go out and measure the heights of 10 college students. That's data. Or I can collect them as responses. I can ask 10 people what their favorite ice cream flavors are, and that's also data as well.

Now one of the fundamental challenges of working with data in statistics is that oftentimes I can't go out and ask every single person and collect data from all the people I'm interested in talking to. Instead, I only have to focus on a smaller group. We have two words to describe those two different groups of people. The first one is called a population. This is a set that contains all of the data, all of the measurements and counts or responses that you have from all of the people you are interested in talking to.

This would be like if I went and measured the heights of every single college student in the entire United States. Now, obviously, that is incredibly impractical, and I can't do that. So instead, I just focus on a smaller group of people called a sample. So this is basically just only have a part of a population or a subset. The idea here is that if I grab a sample of a hundred college students and if I only just focus on that, that will give me some information and help me learn about the wider population.

Alright? Now there are two other words we're going to talk about later on, but we actually can just jump straight into our example here. So let's get started. So with our example, what we're going to do is, for a and b, these two boxes over here, we're going to label each dataset as being from a population or a sample. So let's get started.

So for part a, what we have is this box here, and it says the salary of every employee at a marketing firm. Right? So salary is just a piece of data, and it pertains to a group. Right? Every employee at a marketing firm.

Part b says the salaries, same data, from 12 out of 100 total employees at a marketing firm. So which one do you think is the population and which one do you think is the sample? Well, again, these keywords that you're going to see that are dead giveaways that you're talking about a population are words like every and each. Right? This is the salary of every employee at a marketing firm, and so this is the population.

Now, you might think that a population just means that we're going to be looking at the salaries of every single marketing employee from the entire country, but it doesn't always have to be as massive as that. In this case, we're only just interested in the salaries of every employee at this specific marketing firm, which is still a population. Right? And this is a sample because, usually, we're given, you know, some number out of a total number of people that are within this population, so this is a sample. Right?

So that is the difference between sample and population. So you can kind of think about it as a population. It's like the sort of big red bubble over here that contains everybody in the company. But, again, taking the salaries of a hundred employees can be a little bit impractical. So the idea is we're going to use the small sample of 12 people to get some information about the wider population.

Okay? So now let's take a look at the second sort of pair of words that we'll be working with, which is called parameter and statistic. Now a parameter is a single number that you observe from, and it's going to be a population. This would be, for example, like an average height of all the college students that I measured the heights of. Or if I said, for example, 30% of people preferred vanilla ice cream, that would be a parameter.

A statistic is basically the same idea. It's a number that you observe, but not from the population, but it's from the sample. There's a very, very easy way to remember these and never get confused. P always goes with p, so population always goes with parameter, and s always goes with s. So population parameter, sample statistic.

Right? If I talk about the average heights of everybody in the entire country, that's a parameter. If I talk about, well, at least 12 out of 100 employees or something like that, or let's say 10 out of this group of college students and 30% preferred vanilla ice cream, that's a statistic. All right? So now let's go ahead and take a look at our second pair of boxes here.

For C and D, what we're going to do is we're going to label each number as a parameter or a statistic. Okay. So what we have here is, at the bottom, we've got the average salary of all employees at a marketing firm is $41,000 And then this last one over here for part D, what we have is the average salary of 12 out of 100 employees at a marketing firm is $58,000 So hopefully, you see what's going on here. The average salary, again, this is just the single number that represents or that you're going to be observing from the entire population, which is all employees. This is referencing this population over here.

So therefore, this is the parameter. Alright. And then and that number here is $41,000 However, when we take only just a small subset of people, the 12 out of 100, we found that the average salary is $58,000 Notice how those two numbers are not the same, and oftentimes in statistics, they won't be. And that's one of the challenges. So this is a statistic and this is a parameter.

Again, it's the same idea here. This parameter is if you grab the salaries of everybody at this marketing firm, it would be that number. But if you only just focus on this group of people, it would be $58,000 Okay? So that's the idea, folks. That's the basic difference between parameter and statistic.

And now that we know the difference, let's take a look at some practice. Thanks for watching.

You collect the test scores of every other student in a class. Is this data set a population or sample?

• A. Population
• B. Sample

Answer: (B)

A report shows the amount (in dollars) spent by each customer in a grocery store. Is this data set a population or sample?

• A. Population
• B. Sample

Answer: (A)

46.5% of all registered voters in a country are registered democrats. Is this a parameter or a statistic?

• A. Parameter
• B. Statistic

Answer: (A)

A survey of 40 gym members from a large gym finds an average work out duration is 52 minutes. Is this a parameter or a statistic?

• A. Parameter
• B. Statistic

Answer: (B)

Types of Data

In recent videos, we've talked a lot about data, which is really just information that you gather from populations or samples, and we talked about the difference between those two terms. Now I used some examples of data like the heights that you would measure from college students or their favorite ice cream flavor, but those two sets of data aren't exactly used the same way. With heights, I can do calculations with them and things like that, whereas with the ice cream flavors, they have a little bit more limited uses. So data can be categorized in two different ways, and those categories are basically called qualitative or quantitative data. You'll need to know the difference between these two, so I'm going to show you a bunch of different examples of this, and then we'll do some examples together.

Let's get started here. So, basically, qualitative data is just where the data are qualities, as the name implies. In other words, they're basically just names or labels or kind of like attributes. So one example that we've used already is if I asked a bunch of students their favorite color, that's just a name. You can't really attach a number to that.

Another example of this is if you go around and ask or survey people's eye colors, it's just going to be, you know, one, like, blue or brown or something like that. Right? Those are just names or labels. These are attributes. So this is qualitative data.

These things have limited uses because you can't really do calculations with them. All you can do is kind of just organize them into their own little qualities or categories. Now on the other hand, we have quantitative data. And most of the time in this course, we're going to be working with quantitative data. This is where data are quantities, not qualities.

In other words, these are basically you have numbers or you have measurements. Now within quantitative data, that actually breaks down into two slightly different categories called discrete versus continuous. Now the way I like to think about discrete is that these numbers cannot be broken down any further. Alright? So think about like a dice roll. If I roll a dice, the only six options I can get are one, two, three, four, five, and six. I can't roll the dice and break that number down into, like, a 1.2. So this is what's called a discrete, quantitative variable. Right? This is basically where you can kind of count up the total possible outcomes that you could have.

Another example of this is if you were to survey a classroom and figure out the number of students, you can't have 1.4 students in a classroom. So these are things that basically are countable. Alright? That's another word that you might see for this. A continuous variable, on the other hand, is where numbers can be broken down even further.

And two classic examples of this are time and temperature. For example, time, if I were to measure, let's say, the time that somebody's running a race, if I have a powerful enough stopwatch, I'd be able to break that down not only into hours, but then minutes and seconds. And I can keep even going into decimals, like microseconds and things like that. Right? You can get down into the nitty gritty of those decimal places because you might have powerful enough instruments to do that.

The same thing applies with temperature. These are things where, basically, you can further subdivide these numbers into decimals and fractions and things like that. That's a continuous variable. That's really all there is to it, folks. So let's just go ahead and do a couple of examples together.

So we're going to determine whether the data are qualitative or quantitative. And if it is quantitative, we're going to figure out if it's discrete or continuous. So let's take a look at the first one here. You're going to survey the nationalities of 10 people on a plane and gather that data. Is that qualitative or is that quantitative information?

So the first thing you should think about, right, is can I attach a number to this or are these things kind of just names and labels? And if we're talking about nationalities, these things are basically just names. Right? It's the country of origin. So this is definitely not going to be quantitative data. This will be qualitative. That's the answer to our first question here. Alright? Now let's take a look at the second one. With GPS enabled watches, you measure the distances that people walk to work each day.

Okay? So the distances, if you're measuring some kind of a distance, that's going to be a numerical number. It's going to be like 10 kilometers or five kilometers or something like that. So it's definitely not qualitative, and it's definitely going to be a quantitative answer. So now we just have to figure, is it discrete or continuous?

And the second question you need to ask is, can I break the number that I measure down even further and further? So for example, can I only walk five or six kilometers to work each day? Does it have to be one of those two numbers? Or can I break that down and say, well, I actually walk 5.3 kilometers to work? And that's actually the right answer.

Right? So this thing is you can break down these numbers even further into, you know, kilometers and even meters or even, like, micrometers if you wanted to get down that nitty gritty. And so this is a continuous variable. This is not discrete. Alright?

Those are the two answers. Let's go ahead and take a look at some more practice problems. Thanks for watching.

Which of the following is NOT quantitative data?

• A. The amount of hours students study per week
• B. The heights of basketball players (in centimeters)
• C. The brands of smartphones owned by students
• D. The outcomes of ten rolls of a standard six-sided die

Answer: (C)

Which of the following is a discrete quantitative set of data?

• A. The weight (in kg) of a bag of apples in a grocery store
• B. The temperature (in °C) in a classroom
• C. The time (in seconds) it takes for a swimmer to complete a lap
• D. The number of goals scored by a soccer team in a match

Answer: (D)

Here’s what students ask on this topic:

What is the difference between a population and a sample in statistics?

In statistics, a population refers to the entire group of individuals or items that you are interested in studying. It includes all members of a specified group. For example, if you are studying college students in the United States, the population would be all college students in the U.S. A sample, on the other hand, is a subset of the population. It consists of a smaller group selected from the population, which is used to make inferences about the population. Sampling is often necessary because it is impractical or impossible to collect data from every member of a population. By analyzing a sample, statisticians can estimate population parameters and make informed decisions.

How do you differentiate between qualitative and quantitative data?

Qualitative data refers to non-numerical information that describes qualities or characteristics. It includes attributes, labels, or categories, such as colors, names, or types. For example, eye color or favorite ice cream flavor are qualitative data. Quantitative data, on the other hand, involves numerical values that can be measured or counted. It is further divided into discrete and continuous data. Discrete data consists of countable values, like the number of students in a class, while continuous data can take any value within a range, such as height or temperature. Understanding these distinctions is crucial for selecting appropriate statistical methods for data analysis.

What is the difference between a parameter and a statistic in statistics?

A parameter is a numerical characteristic or measure that describes an aspect of a population. It is a fixed value, although it is often unknown and needs to be estimated. Examples include the population mean or population proportion. A statistic, on the other hand, is a numerical characteristic or measure that describes an aspect of a sample. It is calculated from the sample data and used to estimate the corresponding population parameter. For instance, the sample mean or sample proportion are statistics. The key difference is that parameters describe populations, while statistics describe samples.

What are discrete and continuous variables in quantitative data?

In quantitative data, discrete variables are those that can take on a finite or countable number of values. They are often whole numbers and represent countable items, such as the number of students in a class or the number of cars in a parking lot. Continuous variables, on the other hand, can take on an infinite number of values within a given range. They are measurable and can include fractions or decimals. Examples include height, weight, and time. Continuous variables allow for more precise measurements and can be subdivided into smaller units, unlike discrete variables.

How can you determine if data is qualitative or quantitative?

To determine if data is qualitative or quantitative, consider whether the data represents attributes or numerical values. Qualitative data consists of descriptive attributes or categories, such as names, labels, or qualities, and cannot be measured numerically. Examples include hair color, nationality, or brand names. Quantitative data, however, involves numerical values that can be measured or counted. It includes data that can be expressed in numbers, such as age, height, or temperature. If the data can be used for mathematical calculations, it is quantitative. Understanding the nature of the data helps in selecting appropriate statistical methods for analysis.