The data set represents the number of movies that a sample of ...

Question

The data set represents the number of movies that a sample of 20 people watched in a year.

121 148 94 142 170 88 221 106 18 67

149 28 60 101 134 168 92 154 53 66

b. Display the data using a frequency histogram and a frequency polygon on the same axes.

Accepted Answer

Hello. In this video, we are given the following data set of ages and a requirement to use 5 classes, and we want to construct a frequency polygon. In order to start constructing this frequency polygon, the first thing we want to do is you want to go ahead and reorder our list of data from least to greatest. So the list of data from least to greatest is going to be the following. We are going to have 1822, 25, 28, 30, 35, 38, 40, 45, 48, 50, 55, and 60. Now, the reason why we reordered the list from least to grads is because we want to approach this problem by first calculating the width of the classes. Now, the width of the classes is defined as the range of the data set divided by the number of classes we are working with. But the range of the data set is going to be the maximum value minus the minimum value. So let's go ahead and identify the maximum value first. Now the maximum value is the last number in the data set, and that is going to give us a maximum value of 60. The minimum value is going to be the 1st value in the data set, and that is going to be 18. So the range is going to be defined as 60 minus 18, and that is going to give us a range of 42. Now, what about the number of classes? Well, the problem tells us that we are required to work with 5 classes, so the number of classes we are going to be working with is 5. So our width is going to be defined as 42 divided by 5, and that is going to give us an approximate width of 8.4. Now in this case here, because we are trying to construct a frequency polygon, our width needs to be a whole number. So when we have a decimal as a width, we just want to round to the next integer. So our width is going to be 9 in this case. Now that we've determined the width of the classes, the next thing we want to do is we want to go ahead and construct a frequency to class midpoint table with respect to the class limits. So let's go ahead and create that table. We're going to have class limits. We are going to have our frequency. And we are going to have our class midpoints. So Let's go ahead and construct our first class limit with a width of 9. We are going to start with our minimum value, which is 18, and we want to have 18 as our first value with a width of 9. So the first class limit is going to be 18 to 26 since that has a total width of 9. Repeating this process with the next value, we are going to have a class limit from 27 to 35. Then we're going to have 35 or 36 to 44. We will have 45 to 53. And finally, we will have 5354. 262. Now let's go ahead and determine the frequencies of each of the class limits. So for the first row, we want to determine the frequency between 18 to 26. What this means is we want to take a look at the data set and ask ourselves how many numbers within the data set fall within the range between 18 and 26. Well, in total, there are 3 values that fall within this range, so the frequency from 18 to 26 is going to be 3. And the midpoint between 18 and 26 is going to be 22. Next, for 27 to 35, the number of values that fall within this range is going to be 3, and we will have a midpoint of 31. Again, repeating this process, the number of values between 36 and 44 is going to be 2, with a midpoint of 40. The number of values between 45 and 53 is going to be 3, with a midpoint of 49. And the number of values between 54 and 62 is 2 with a midpoint of 58. So what we've created here is a frequency versus class midpoint table. And so let's go ahead and move this table to the top next to. The polygon table. Now, in this case here. The two columns we want to focus on is the frequency column versus the class midpoint problem or column. So let's go ahead and clear up everything else. Now, what we're going to do is we're going to label our class midpoints on the X axis of the polygon of the frequency table. So the first class midpoint again is 22, which is going to be roughly here. The 2nd class midpoint will be 31. The next class midpoint will be 40. The next one will be 49, just before 50. And the last one will be 58, which is right before 60. Now, when creating the frequency polygon, we also want to include two additional points which are called anchor points. Now, anchor points are going to be zero values that occur before the minimum value and after the maximum value. Now again, our minimum value of the data set is 18, so we can go ahead and set an anchor point at 15, which is the halfway point between 10 and 20. And our maximum value is 60, so we can set an anchor point somewhere after 60, let's just say 65. So these are going to be zero values for the frequency polygon. But now what we want to do is we want to go ahead and label the value of the frequency for each of the midpoints. Now, 22, our first midpoint, had a frequency of 3. So that is going to have a tip of the frequency polygon here. And again, you just have to do your best to draw this out. Now, at the next midpoint, we also have a frequency of 3. The midpoint F44 has a frequency of 2. So here, The next midpoint has a frequency of 3 at 49. And the last frequency of 58 has a frequency of 2. And so what we need to do now is we just need to connect all of our red dots together. And this is going to construct the frequency polygon for us. So this is going to be the approximate shape of the frequency polygon, but the correct solution to this problem is going to be option B. So I hope this video helps you in understanding how to construct a frequency polygon, and we will go ahead and see you all in the next video.

The data set represents the number of movies that a sample of 20 people watched in a year.
121 148 94 142 170 88 221 106 18 67
149 28 60 101 134 168 92 154 53 66
b. Display the data using a frequency histogram and a frequency polygon on the same axes.

Key Concepts

Frequency Histogram

Frequency Polygon

Data Grouping and Class Intervals

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