## Statistics How to make a histogram

Welcome to MySecretMathTutor, in this examplewe are going to make a histogram. Now you may have heard of these before, ormaybe even seen them, and said, quot;Hey wait a minute, that thing looks like a bargraph.quot; Well histograms are a bar graph, but theyare a very special type. They give us quantitative information, so they give us a lot about thedistribution of the data, and tell us basically how many are in each category.So for this example I have a collection of different numbers, and we are going to createa histogram for this data. Now one thing you want to identify is thevalues that should go along the bottom and

the values that should go along the side.Along the bottom we put the values of our variables.So what things are we talking about. It looks like we are talking about some 7s, 8s, 9s, 10s, all that good stuff. So I will put that along the bottom.Perfect. Ok Now along the vertical bar, this is wherewe put our frequency. In other words how many of these things do we haveĆ© Well lookingat all of my data, it looks like the smallest number of things is like only one of them.And the maximum number of things I have is 1, 2, 3, 4, 5, Oooo, 5 eights.So I want to make sure that my scale over here

has enough to handle at least 1, 2, 3, 4,5 things. There we go.So again this represents frequency, and this represents the values of our variables.Ok, so let's start off. How many 7s do we have. It looks like we have1, 2, 3. So in my 7 category, I will create a bar thatgoes up to 3. Just like that.When I get to my 8 category I count up how many of them I have. 1, 2, 3, 4, 5. And Imake a bar that goes up to 5. And you can see how this process plays outfor all of the rest of the numbers.

So when I get to the 9s, I only have one 9.When I get to the 10s, I have three of those. I get to the 11s, I have two 11s. Looks likethree 12s. And only one 13. So now we've created different bars for ourhitogram, and you can see which variable is the most frequent. It's basically the tallestbar. And there you go.For more tutorials please visit: MySecretMathTutor .

### How to Find Any Limit mathbff

Hi guys! I'm Nancy and I'm going to show you how to find the limit at a value, at a finite value. Limits are kind of a mess, so I made a couple tutorials and here are some links to my other tutorials If you just want an introduction to the limits, what do they mean check out the introduction tutorial. If you are looking for how to find the limit at infinity check out the limits at infinity tutorial.

But this is how to find the limit at a value, at a finite value so let's look at the types I'm going to cover. OK, these are the first four of seven ways to find the limit at a value, a finite value. They are the four main ways, most common strategies. If you already see the kind you're wondering about the kind of problem you're working on, you can skip ahead. You can use the links in the tutorial to skip directly to that part

or you can check the description to find the exact time to skip to. So let's look at them. The first is to plug in, if you can. If you can't, and I'll show you why you might not be able to. try factoring, if possible. If not, see if you can get a common denominator. That means if you have something that looks like a fraction within a fraction a complex rational expression you might be able to get a common denominator.

If not, see if you can expand. Open up parentheses and expand simplify and then find the limit. These four cases cover most of the kind of limit problems at a finite value that you would get. Ninety percent of them. But there are a few oddball, miscellaneous, misfit cases that come up. so let's look at those OK, these are the three miscellaneous, oddball cases.

If you're looking for one of these, I lied. They're not actually in this tutorial but you can use the links in this tutorial to jump to that tutorial where I explain these or look in the description for the tutorial link. Basically, if you have a square root in a fraction, in the numerator or something like sin x over x, or absolute value, you'll need these strategies but forget about those for now. Let's look at the four most common strategies. OK, with these limit problems, the first thing you should always try is to plug in the value. Plug in 4 for x

everywhere x appears, and see if you get a value for the limit. OK, so you got an actual number for the limit, a finite value fivesevenths, is a finite unique number. That is your limit. The limit is equal to fivesevenths, and you're done. But if you ever get a zero in the bottom, in the denominator or the form zero over zero, which is indeterminate you have not found the limit. You're not done, you'll need another way, another technique.