In this video, we will be finding class with making a frequency table. Taking the information from the frequency table to make a history graham. A relative frequency hissed a gram and no jive and then to discuss the distribution as well as interpret the graphs that we make. So this is a long video. I'm going to do my best to shortcut a couple places to hopefully keep this as close to 10 minutes as possible. So I've taken the liberty of taking the information and putting in order from least to greatest. This is information from usa today from 50 colleges and universities where they did a survey and asked what percent of your enrollment were males. So 26 would mean in this particular college, 26% of the enrollment or males here, this particular college or university, 48% of the enrollment or males. We're asked to find the class with based on the fact that we have five classes. Remember class with is the distance between the lower class limits A. K. A. The values that will make up our our graph are intervals for our graphs And for our charts. So we take the maximum value which in this case is 79. subtract the minimum value And divided by five because that was already predetermined for us that we would have, we would have five classes, that's 53 divided by five And that's approximately 11. So our class width will be 11. Now I'm gonna take that information and that's going to help me make my chart so you can see here I gotta started my class limits. My lower values are in red notice I started with 26 because 26 was my lowest number. Now to go from one class to the next, I need to add 11 because that was my class with 26 plus 11 is 37 37 plus 11 is 48, 48 plus 11 is 59, plus 11 is 70. Then I simply finished the upper class limits by looking here because they have to be consecutive, 36 is in front of 37 47 48 58 59 69 70. And then I go to 80. And the reason why I know it's 80 is because if you look back you can see The interval is 10 units across, So it's 10 units then plus one to get to the next class. Now my class boundaries are found pretty easily by adding or subtracting 0.5. So if it's a lower limit, I subtract 0.5. If it's the upper limit, I add 0.5, So 26 minus 260.5 is 25.5, 36 plus 360.5 is 36.5. And then actually comes pretty easy after that because these two values will always be the same. And then if you notice 25.5 plus 11 is 36.5. So this will be 58.5 69.5. And then we go to my next slide and show you the final result of my class boundaries. Please feel free to pause the video. But again, I'm trying to do this quickly so that we can finish it in a reasonable amount of time. The next thing I need to do is I need to tally up the values so that means to go back to my original list and count up how many numbers fall in this range. So if I go back to the original list, I can see I have 26. So these are the values that fall within 26 and 36. There are four of them. That is why I had four tally marks. And then my frequency is the number of items that fall within those limits. So that would be four. So when I go back to my information and I count up all the values in the next class, which will be 37. All the way to 47. I need to count up all these numbers. And when I count up all those values I will find that I have 21. Then my next class was between 48 and 58. So I need to count up all the values in between And then there's my 4th class and here's my 5th class. So when I do the tally sometimes that's an easy way to keep your information organized or you can just count it up. But here are my tally marks. Remember each of these represents 1, 2, 3, 4 and then you cross over to make it five and then my frequency is just the total. So again two numbers in my data set fell between 70 and 80 and this is going to be the vertical axis when we make our history. Um and then our class boundaries will buy our horizontal axis. The next thing you are asked to find is the midpoint. That means you add the two limits together and then divide by two. So 26 plus 36 divided by two is 31, 37 plus 47 divided by two is 42. Again feel free to pause the video just trying to get this all done under the 10 minutes 48 plus 58 divided by two is 53, 59-69 divided by two is 64. So again, I'm just adding these two values together and then dividing by two to find the point that's halfway between them or the midpoint. We're not going to use the midpoint for the rest of this question, but it is asked for and later on you might use it in some of your graphs. Now, relative frequency is where we take the frequency and we divided by the sample set total and this case is 50. So to find the relative frequency for the 1st 14 divided by 50. And that will give me 0.08, 21, divided by 50 0.42, 22, divided by 50.44 One divided by 50 0.02 and two divided by 50 0.04. And then the cumulative frequency is taking the frequency and adding up the values as we go along. My first is four. Then I do four plus 21 25 plus 22. That's where 47 comes from. 25 plus 22, 47 plus one is 48 48 plus two is 50. And notice how our last value is actually the total in our sample set. Now we're asked to make a history graham. So these class boundaries will be our horizontal axis. And then I will use these for my hissed a gram and I will use these for my relative frequency hiss to graham. So again in my history Graham, this is a graph where the bars touch and the bottoms are intervals. So my horizontal axis will simply be the lower class limits. So that it would be 25.5, 36.5, 47.5, 58.5 69.5 And then 80.5. And then you can choose whatever increments you want. As long as they are equally spaced, your increments will determine how your graph looks. I chose to go up by five Because you remember my largest frequency was only 22. So my first category, my bar would go up to four. Honey would shade it in the second category or class went up to 21. The third one was about 22. The fourth one was one and the fifth one was too. Again, feel free to pause the video and I will go when I go to the next slide I will give you the finished values. That's kind of hard to do this by hand. But now the next hissed a gram requires me to do a percent. That's what relative frequency basically is. It's a percentage in decimal form. So across the bottom my intervals are all going to be the same, but now I'm going to use a percentage. So if I go back to my other screen I need to take this value and I need to change it to a percent, which is pretty easy to do. I can multiply this decimal by 100 or some of you might be able to see that 50 goes on 102 times. But usually what's done is you take the decimal. So in this case 0.08 multiply it by 100. That will give you 8%. So my, my graphs, I chose to go up by tens, but now these represent percentages. So my first category would go up to about 8%. My second category was 0.42. So when I multiply that by 100 I get 42%. So about 40 to 44, two and 4 again, Because 0.4, four times 100 is 44, 0.2 times 100 0.02 times 100 is two and 0.4 times 100 Is 4%. Now I'm going to go on to the next slide so I can show you the final result. Notice they look the same and that's just because that's how I chose to make my increments that they were equivalent. Now I'm asked to describe the distribution. So if you look at your graphs here, you can see that I have this big mound and then it tapers off and kind of tapers off to the right. This is what we call skewed, right? Because you most likely have an outlier over here or most of your data is on the left again, pause the video if you need to to look at some of this and copy it down. But we say that our data is our graphs are skewed right now. The next thing that you're asked to do is you're asked to find an O jive Now, uh no jive is just a graph that displays the cumulative frequency. So when you go back to the chart here are cumulative frequencies for 25, 47, and 50. So when I make my oh jive, the numbers across the bottom are the same. I chose to go out by 10s. So I start here with a zero because that's how much I've accumulated at 25.5. Then at the end of the interval 36.5 I have four values. So I plot that connect the dots at the end of 47.5 I have 25 total Plot that connect the dots at the end of 59.5 I have 47, connect the dots add 1 48 and add 2 to 50. So this is my oh jive. This is the graph that displays the cumulative frequency. And then finally I am asked to interpret my graph. So if I go back to my history grams, I can see Remember this represented 42% and this represented 44%. So I can see most of my information is between these two values. In between these two intervals 36.5 and 58.5. And in fact 42 plus 44 is 86. So that's 86 of my information of my graph, of my data falls between those values. So if we put it back in the context of this particular problem, and again, this these answers can vary according to our relative frequency, hissed a gram. Oops! I spelled, hissed a gram wrong. Sorry, there's no are there hist a gram, 86% of the colleges and universities in our sample had between 36 a half percent and 58 a half percent of their enrollment be males. That doesn't sound very grammatically correct, But 86% of the colleges had between 36.5% and 58.5% of their enrollment ended up being males. And then I could also say that it's unusual for these college and universities to have more than 58.5% of the enrollment turned out to be males. So remember we didn't have very much on our graph, we only had three colleges that had any enrollment greater than that.