Transcription
In the lesson of statistical graphs, we're going to review different types of graphs to use in statistics and determine which one might be suitable for representing a specific set of data. The graph should be effective in revealing the important characteristics of the data.
So this is a frequency polygon. As you can see, when we connect all of these dots, we always start down at zero and then we go to the first midpoint of each class and then we connect midpoints of the classes and then always go down one more to zero again to one beyond the last class of your data. So as you can see, this forms what looks like to be a polygon.
Now, if you remember, relative frequency polygons focus on the proportion or percentages of the frequencies, and we can combine on the scale of polygons one for women and one for men so that we can view them together in a graphical form. So this combines two relative frequency polygons onto the same graph.
This is an ogive. This is a line graph that depicts cumulative frequencies, so adding on from the previous value. So at 69.5 pulse rate, we have it looks to be probably around 15. Then the next time we add on to the 15, the next frequency of 79.5. So 26 of the values are less than 79.5. So we keep adding on to the 15. So that would mean this frequency at 79.5 is probably around 9 because 15, if I'm guessing here, 15 plus 9 gives us the 26 cumulative value. Adding, think of accumulating, adding previous, uh, frequency.
Let's use this ogive to determine the frequency of the one to 1.99 pound class. So 1.995 would be that midpoint. That looks to be about 34, but remember this is cumulative. So 34 includes everything from 0 to 1.995, that midpoint of of where our data is. So we need to subtract what it is below that. We know that zero over here for our polygon, but this looks to be about 14 or 15. Let's say 14. So 34 minus 14 equals 20 in 1.1 to 1.99 class only because we are accumulating. We added to the 14, 20.
A dot plot is where each data value is plotted as a point or a dot. So in this particular case, at 60, we have three frequencies. At 16, we can count the dots to find out the frequency of each pulse rate. This really gives a good a picture of possible outliers and what kind of spread we have, if we're skewed left, skewed right, and things like that. So it's a good visual. Dot plot gives you a good visual of the frequency.
Now, a stem plot represents quantitative data by spreading each value into two parts. One part is the stem, which is the leftmost digit of your number, and the other part is the leaf, which is the rightmost digit of your number. So when we look at this, it's like splitting it up between 60s, 70s, 80s, 90s, 100s. So it's it kind of looks like 110s, 1, 12. It kind of looks like, um, classes like we've divided it by classes, but we're making a stem and leaf plot of the 60s through one. Sorry, that's supposed to be 120s, not 1, 12. So for example, this list of numbers here would say that I have 360s in my data because there's three zeros behind the six. I have four 64s and 56. Okay, so that's and then 72. I got a lot of 72s, 76s, 80s and 88s, 196. So there's one in the 90s, one in the 100s. This is a typo here. This is supposed to be 104, and then this is supposed to be 124.
A township recorded the temperatures once a week for 12 weeks. Use the temperature shown below to construct a stem plot. So we need to make our stems and our leaves. This data looks to be 50s, 70s, 80s. I would start my stem, my first stem in the 50s and then go up 10 each time. So let's do 5 for 50s, and I have in order, we want to go from least to greatest. So 54 first, then 55, and then 59. Next, we'll look at the 60s. 60s, I have 65 and 68. So we will put a 6 for 60, and we'll put in order 5 and then 8. Then we'll look at the 70s in order. I only see 170. So we'll put 72. 80s, I have 80, 86, 85. So for the 80s, I have 80 and in order 85 and then 86. And then last but not least, I have those 90s left, and in order it would show up as 90, 92, and 93. And how many numbers you have, you always make sure you keep them in nice even columns so you can get a visual. I know that I have probably about the same amount of 50s and 80s and 90s, obviously less 70s and 60s based on the length of these, uh, leaves.
In a bar graph, bars of equal width are used to show frequency of categories of qualitative data, so meaning categories, not numbers. The vertical scale represents frequency or relative frequency, when the horizontal identifies different categories of qualitative data. Uh, we can combine bar graphs as well, two or more sets of bars to compare two or more sets of data, such as male to female for gender and income. How do male and females do their income compare in the 1950s versus the 2000s? What is the average income for males versus male, uh, females? Notice how the bars don't touch, per catego, touch different categories, I should say, leave some space between your categories because a histogram is when we, the bars actually touch each other.
Here we have what's called a back-to-back and leaf plot. We want to determine the total number of women with a pulse rate greater than 80 in this stem plot. So 80 is right here, and women is on the left side. So 80 greater than 80, that would include 88, and then 96, 104, and 124. So adding those numbers up, we got one, two, three, four, five, six, seven, eight women with a pulse rate greater than 80.
A Pareto chart is a bar graph for qualitative data. The bars are arranged in descending order according to the frequencies. So this specifically has to go in an order of which one is the highest to the lowest, descending order.
Pie graphs should be used to depict a qualitative data in slices of a circle. So all together, all the pieces or slices need to add up to 100%. Cannot have less than 100 or greater than 100 because the whole pie is 100, and these are going to represent each proportion of the frequency count. I should add in this word here: all slices together add up to 100.
The scatter plot, uh, pairs data X and Y with a horizontal and a vertical axis. It's used to determine whether there is a relationship between two variables. So scatter plots, we're looking for a relationship. Does it look like they're related to each other based on how it's plotted? So chirps per minute is a numerical representation and temperatures. So if I hear more chirps at a certain temperature, you'll see that some kind of correlation, if chirps are related to temperature.
So while we're describing data using a histogram, would be a good idea to consider the distribution, center, variation, and outliers. We look for features of the graphs that reveal some sort of useful and or interesting characteristics of the data. When comparing data, construct similar graphs to compare data. You remember that we use either two bar graphs next to each other or two polygon and polygon frequencies next to each other, some way to compare your data and visually.