Speaker A
welcome to anywhere math. I'm Jeff Jacobson, and today we're going to begin a very interesting topic. Today we're talking about an introduction to statistics. Let's get started.
Jeff Jacobson of Anywhere Math introduces statistics as collecting, organizing, analyzing, and interpreting data, then works through dot plot examples on mouse weights and student heights.
Key Takeaways
- Statistics is about collecting data and using it to answer a question
- A statistical question should produce a variety of answers, not a single fixed one
- Dot plots display data on a number line with dots representing each value, and should be labeled with units
- Clusters, peaks, and gaps in a dot plot reveal the distribution and tendency of the data
What the video covers
- Introduces statistics as the science of collecting, organizing, analyzing, and interpreting data
- Explains that data must first be collected through surveys or experiments before analysis
- Describes organizing data by ordering it, using tables, or making graphs
- Defines a statistical question as one that yields a variety of answers with an interest in distribution and tendency
- Distinguishes a statistical question from a survey question asked of individuals
- Analyzes data using mean, median, mode, and range to understand its overall character
- Example 1: determines whether 'What is the weight of a mouse?' is a statistical question (yes, since weights vary)
- Example 2: builds a dot plot of mouse weights in grams, labeling the axis and units, and checks that dot counts match the data
- Identifies clusters, peaks, and gaps in dot plots, such as a peak at 20 g and a gap between 23 and 27 g
- Example 3: uses a dot plot of student heights to count students (22) and describe where most students cluster (around 156 cm)
Chapters
Full Transcript — Download SRT & Markdown
Speaker A
exactly statistics is so statistics is the science of collecting organizing analyzing and interpreting data it's all about data well first you got to collect data data just doesn't appear you got to collect it somehow maybe you do a survey
Speaker A
All right, for the introduction to statistics, let's first define what exactly statistics is. So, statistics is the science of collecting, organizing, analyzing, and interpreting data. It's all about data.
Speaker A
maybe from least to greatest that's a common thing to do at the start uh maybe you'll put them in a table maybe you'll make a graph well then you analyze it what is the data telling us we do things
Speaker A
Well, first you've got to collect data. Data just doesn't appear. You've got to collect it somehow. Maybe you do a survey and get data that way. Maybe you perform some experiments, and you measure and record data as you go along.
Speaker A
tried to analyze it somehow how does that help answer whatever questions we were looking for answers for okay that's what statistics is all about it's all about collecting that data and using it to help answer a question so statistics
Speaker A
Once you have the data, what do you do with it? Well, we organize it. Put it in order, maybe from least to greatest. That's a common thing to do at the start. Maybe you'll put them in a table. Maybe you'll make a graph.
Speaker A
answers you're not expecting just a couple different options right uh and you are interested in the distribution and tendency of those answers now one more thing I want to add about statistical questions don't get confused from a survey question and a statistical
Speaker A
Well, then you analyze it. What is the data telling us? We do things like find the mean, median, mode, or range to get a sense of what the data is all about.
Speaker A
say how much do you weigh and you go to the next person how much do you weigh and all the sixth graders you're going to survey you ask them how much do you weigh that would not be a statistical
Speaker A
Then we interpret that data. What does it tell us? Now that we know and have all this data, and have tried to analyze it somehow, how does that help answer whatever questions we were looking for answers to?
Speaker A
is the weight of a mice Mouse okay well first is this a statistical question and if so explain now if you remember from the definition statistical questions should be giving us a variety of answers uh they should be able to show us a
Speaker A
Okay, that's what statistics is all about. It's about collecting that data and using it to help answer a question. So statistics is all about answering a question.
Speaker A
same they're going to be different just like humans are going to weigh different amounts same with mice so our answer yes because you would expect the weight of mice to vary let's try Part B okay Part B so we weighed a whole bunch of mice
Speaker A
Well, first, what exactly is a good statistical question? A statistical question is one where you expect to get a variety of answers. That's really big: a variety of answers, a whole range of answers. You're not expecting just a couple of different options, right? And you are interested in the distribution and tendency of those answers.
Speaker A
about the data right we've already done that first step collecting the data now we're going to organize it uh and we're going to make a uh a dotplot uh and then after the dot plot's made identify any clusters Peaks or gaps and we'll talk
Speaker A
One more thing I want to add about statistical questions. Don't get confused between a survey question and a statistical question. For example, if your statistical question was, "How much do sixth graders weigh?" that's your statistical question. But when you do the survey, you're not going to ask people, "How much do sixth graders weigh?" You're going to say, "How much do you weigh?" and then you go to the next person and ask, "How much do you weigh?" and all the sixth graders you survey, you ask them, "How much do you weigh?" That would not be a statistical question, but it's going to help us get data to answer the statistical question.
Speaker A
like a little bit like a bar graph except with dots instead of bars um so we're going to start with a number line well if I look at my data I can see that uh the least value is 18 uh
Speaker A
With that, let's get to our first example.
Speaker A
values mean so these were all weights so I'm going to label that over here to the side weight and that was in GRS really important to label don't forget that or else nobody's going to know what those values represent uh and then we just
Speaker A
Okay, example one. Let's say your science teacher asks you to do an experiment about mice, and she asks, "What is the weight of a mouse?"
Speaker A
look there were three so I'm going to do one 2 three like that and we'll keep going um at this point you'll notice there were no 24s no 25s no 26s so I'm going to put nothing there and then I
Speaker A
Okay, well, first, is this a statistical question? And if so, explain. If you remember from the definition, statistical questions should give us a variety of answers. They should be able to show us a distribution and a tendency. So we have to think: if I'm doing an experiment with mice, is this going to give me a variety of answers? The answer is yes, because you can't expect all mice to weigh the same. They're going to be different, just like humans weigh different amounts. Same with mice. So our answer is yes, because we would expect the weight of mice to vary.
Speaker A
data values so just count your dots and make sure it matches uh the values over there so I've got one two 3 four five 18 19 20 and if I look at uh that little chart I have 20 values there so I'm
Speaker A
Let's try Part B. We weighed a whole bunch of mice and collected that data, and have it in this little table over here. What we're going to do is display that data in a dot plot. It looks kind of confusing, and it's hard to tell anything about the data yet. We've already done the first step, collecting the data. Now we're going to organize it and make a dot plot. After the dot plot is made, identify any clusters, peaks, or gaps. We'll talk about what those mean in a second.
Speaker A
notice well it looks like there's a whole bunch of data values right there you you're just going to pick kind of what's in the Middle where they're kind of all seem to kind of be drawn to so that would be 20 uh so that's a cluster
Speaker A
But first, the dot plot. A dot plot is basically a number line, which could be horizontal or vertical, and you use dots to show where the different data values are. It's a little like a bar graph, except with dots instead of bars.
Speaker A
that is that's just are there any things where it's the tallest so right here again 20 there is a Peak at 20 and same thing it's possible to have more than one Peak if for example 21 also went up
Speaker A
So we're going to start with a number line. If I look at my data, I can see that the least value is 18 grams, and the greatest is 28 grams. That's where I'm going to start on my dot plot. I have my number line done, all the way from 18 to 28. I need to label what these values mean. These were all weights, so I'm going to label that over here on the side: "weight," and the unit was grams. That's really important to label. Don't forget it, or nobody will know what those values represent.
Speaker A
that obviously is right here uh so there is a gap between 23 and 27 okay so that's just kind of helping to uh explain our data a little bit more okay and finally part C use a distribution to answer what is the
Speaker A
Then we just look at the data and put dots. At 18, how many mice weighed 18 grams? If I look at my data, I can count two, so I put one and two, just two dots right above the number 18. I keep going. At 19, there were three, so I'll do one, two, three. We'll keep going. At this point, you'll notice there were no 24s, no 25s, no 26s, so I'll put nothing there. Then I get to 27 and keep going. There are two of those, and finally, 28. One good thing to do before you're finished is double-check that you counted all of the data values. Count your dots and make sure they match the data. I've got one, two, three, four, five, 18, 19, 20, and if I look at that little chart, I have 20 values there. I'm happy with that.
Speaker A
Peak was at 20 uh so that's how we would answer that question here's one to try on your own all right example two the dot pot shows the heights of sixth graders in my math class so here is the Dot Plot you
Speaker A
Now the dot plot is done. Let's go to the next part: identify any clusters, peaks, or gaps.
Speaker A
height so to figure out how many students I just count the dots so let's see we got 1 2 3 4 5 20 21 22 so there are 22 students in my class okay let's try Part B okay Part B
Speaker A
Let's look at the clusters first. A cluster is where a lot of data values are bunched together. If you look over here, you'll notice there's a whole bunch of data values right there. You're going to pick what's in the middle, where they all seem to be drawn to. That would be 20, so that's a cluster. You might be asking, is it possible to have two clusters? Sure. If you've got a big bunch here and another big bunch here, it's possible to have more than one cluster.
Speaker A
write a statistical question you can answer using the Dot Plot and then answer that question so we're writing a statistical question uh it has to be about the Dot Plot uh remember this was about Heights uh of students in my class
Speaker A
Peaks: hopefully you can guess what that is. Are there any spots that are the tallest? Right here, again at 20, there is a peak at 20. Same thing as before: it's possible to have more than one peak. If, for example, 21 also went up to six, we would say there's a peak at 20 and 21. But as of right now, there's only one peak, because that is the tallest.
Speaker A
most sixth graders in my math class if you look uh we have two peaks right here there's 56 and 57 by the way you may have noticed I didn't label every single um every single Dash uh but if you
Speaker A
Finally, gaps. Hopefully that's obvious: spaces between the data values. That's right here. There is a gap between 23 and 27.
Speaker A
157 uh that's also kind of where we have a cluster so we would say um most of the students are what about 156 CM probably are about 156 cm tall hopefully you can see all of that uh that's it for example two here's
Speaker A
That's helping to explain our data a little more.
Topics:statisticsintroduction to statisticsdot plotstatistical questiondata analysisdistributionclusters and peaksmean median mode rangemathematics educationAnywhere Math
