Use the data set and the indicated number of classes to constr...

Question

Use the data set and the indicated number of classes to construct

(c) a frequency polygon,

Pulse Rates

Number of classes: 6 Data set: Pulse rates of all students in a class 68 105 95 80 90 100 75 70 84 98 102 70 65 88 90 75 78 94 110 120 95 80 76 108

Accepted Answer

Hello. In this video, we are given the following data set of test scores and a requirement to use 5 classes. We want to construct a frequency polygon by using the data set of given test scores. So, in order to construct the frequency polygon, the first thing we need to do is we need to organize our data into a grouped frequency distribution table. So what we need to do is we need to go ahead and first find the class width, define the classes, and determine the midpoint and the frequency for the classes. So, by looking at the data set, there are a few things that we can go ahead and determine. First, by looking at the data set, there is a total of 24 scores, so we have a sample size N equal to 24. The minimum value of the data set is going to be 52. The maximum value of the data set is 95. Now, the range for the data set is going to be defined as the maximum value minus the minimum value. That is going to be 95 minus 52, which is going to give us a total range of 43. And the number of classes. That we are working with is given to us as 5 from the problem. We are working with a total of 5 classes. Now how do we calculate the width using this information? While the width is going to be equal to the range divided by the number of classes. That is going to be 43 divided by 5, which approximates to be 8.6. Now in this case here, for the width, we need to go ahead and round up to the nearest whole number, so we're going to be working with a width of 9. So now that we have all this data, we want to go ahead and construct a frequency distribution table. Now in order to construct the frequency distribution table, we want to start with the first class at a minimum value 52 and use a width of 9. So there are going to be three columns for our table. There is going to be the class limits. Which is our ranges We are going to have our frequencies. So how frequent do those numbers pop up in the data set? And we are going to have the class midpoints. Which is the middle value. Now, starting with the minimum value, which is 52. With a range of 9, we are going to have the first class limit be 52 to 60. Then the next class limit is going to be 61 to 69. We will have 70 to 78. 79 to 87. And we will have one more. Which is going to be 88 to 96. Which is the maximum value. And we are going to list our totals at the bottom. Now looking at the data set, how many numbers fall between the range of 52 and 60? Well, that is going to be a total of two values. The number of data points between 61 and 69 is going to be 3. The number of data points between 70 and 78 is going to be 6. Between 79 and 87 is going to be 8. And between 88 and 96 is going to be 5, so we have a total frequency of 24. Now the middle value between 52 and 60 for a data set is going to be 56. The same is true for for 61 to 69, the middle data is 65. The middle point is going from 70 to 78 is going to be 74. The midpoint between 79 and 87 is 83. And finally, the midpoint between 88 and 96 is 92. So, now what we want to do is we want to go ahead and construct the frequency polygon. Now, the frequency polygon is created by plotting the frequency against the class midpoints, and for each class, and then connecting these points with the line segments. To anchor the polygon to the horizontal axis, we want to add an empty class before and after the class and after the last class. So, let's go ahead and organize the data for the polygon now. So we're going to have the class midpoints on the left. And we're going to have the frequency on the right. So, for the class midpoints, we have 47 as an anchor, which is going to be our zero value. We have 56. 65. 74 83 92 And we will use an anchor of 101, which has a zero frequency. Now, the frequencies for 56 is going to be 2, the frequencies for 65 is going to be 3, 74 is 6, 83 is 8, and 92 is 5. So, now let's go ahead and label this onto the polygon. So we're going to start with 0. Our anchors are going to be 47. And 101. And we are going to have 56. 65 74 83 And 92 And now we just have to plot these data points. So for 56, we had a height of 2 or frequency of 2, 65 had a frequency of 3. 74 had a frequency of 6. 83 had a frequency of 8. 92 had a frequency of 5. And our anchors both have frequencies of 0. And so now all we have to do is just connect each of the plot points by using line segments. And so this is going to be the polygon that we want to construct. And the overall solution to this problem is going to be option D. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Use the data set and the indicated number of classes to construct

(c) a frequency polygon,

Pulse Rates
Number of classes: 6 Data set: Pulse rates of all students in a class 68 105 95 80 90 100 75 70 84 98 102 70 65 88 90 75 78 94 110 120 95 80 76 108

Key Concepts

Frequency Distribution and Class Intervals

Frequency Polygon Construction

Data Grouping and Midpoint Calculation

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