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

c. Display the data using a relative frequency histogram.

Accepted Answer

Below there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The following data set shows the number of hours 24 employees worked overtime last month. 1225 33 41 1829 37 44 1534 27 35 16 192430384214 2026 32 39 45 struct a relative frequency histogram with 5 classes. Awesome. So it appears for this particular prompt, we're asked to ultimately create a relative frequency histogram with 5 classes, and that is our final answer we're ultimately trying to solve for. We're trying to create this relative frequency histogram. So with that in mind, our first step in order to solve for this particular problem is we need to determine the range, so we need to find our range. So looking at our data set that is provided to us, we can tell right away that our smallest value is 12 and the largest value is 45. So the range R is equal to 45 minus 12, which will be equal to 33. Fantastic. Our second step now is we need to find the class width. So in order to find the class width, as we should recall, we need to divide the range by the number of classes, which in this case we're told that there's 5 classes, and then we need to round up if necessary. So with that in mind, we'll call the class with CW and the class width. is equal to 33 divided by 5, which is equal to 6.6, which is approximately equal to 7 when we round to the nearest pole number. Fantastic. So now our third step is we need to determine our class boundaries. So as you should recall, in order to do that based on our data points, we need to start at 12 and add the class width to get each class. So when we do, when we do just that, we will find that our first class will be 12 to 18, then 19 to 25. 26 to 32. 33 to 39 and finally 4246. Fantastic. So now, moving right along here, our 4th step is we need to tally the frequencies for each class, meaning, as we should recall, we need to count how many values fall into each class and then we need to calculate the relative frequencies. So with that in mind, what we need to do now is we need to take all of our data points that are provided to us, and we need to arrange them in. Increasing order meaning from smallest value to largest value, and when we do that we will achieve the following. So the data ranged in increasing order will be 1214, 1516, 1819, 2024, 25, 26, 27, 28. Sorry, 20, so it's 27, 29, 30, 32, 33, 34, 35, 37, 38, 39, 41, 42, 44, and 45. OK. So, for instance, for example, for the 12 to 18 class, for instance, it will have 1214, 1516, and 18. So therefore, its frequency will be 5. So F is equal to 5. I'll call frequency F for short. So once again, for the 12 to 18 class, the frequency will be 5. And for the 19 to 25 class, the frequency will be 4. So I was saying frequency is equal to 5, we'll just say frequency is 5 and frequency is 4 for 19 to 25 class. For 26 to 32 class. Our frequency will be 5, and for our 33 to 39 class, our frequency will be 6. And finally, for our last class for the 40 to 46 condition. F our frequency will be equal to 4. Fantastic. So now, moving right along here, our 5th step now is we need to calculate the relative frequencies. So as we should recall, we need to divide each class frequency by the total number of data points. In this case, there is 24 data points. So for example, for the first class, the relative frequency, which I'll call RF for short, is equal to 5 divided by 24, which is approximately equal to, when we round to two decimal places, 0.21. Fantastic. So by repeating the same procedure for the other classes, the relative frequencies will be, so once again for our 12 to 18 class, we'll have a relative frequency of 0.21. And following along, we will have for the 19 to 25 class, we'll have a relative frequency of 0.17. And then for our 26 to 32 class, we'll have a relative frequency of 0.21. And then for our 33 to 39 class, we'll have a relative frequency of 0.25. And finally, for our last class, for the 4246 class, we'll have a relative frequency of 0.17. Fantastic. So now, our 6th and final step is we need to construct the relative frequency histogram, and as you should recall, in order to construct the relative frequency histogram, we need to use the classes that we determined and the relative frequency values. So, with that in mind, as we should recall, along the horizontal axis, we can either label it with the class boundaries or the class midpoints. For this particular histogram, let us label it with the class midpoints, and as we should recall, the class midpoint for the first class would be. 12 + 18, divided by 2 will be equal to 15. So by repeating the same procedure, we will find that the class midpoints are, so going in order for each of our 5 classes for our midpoint, which I'll call MP for short. So 12345, we will find that going in order for the 12 to 18 class, our midpoint is 15, and for our 19 to 25 class or midpoint is 22, for our 26 to 32 class, the midpoint is 29. For our 33 to 39 class, our midpoint is 46, and for our 40 to 46 class, the midpoint or The class midpoint, which I, I called MP but I guess instead of, so we don't get confused, we'll call it CM so class midpoint. So lastly, for the 40 to 46 class, our class midpoint will be 53. And once again, we're just using the same formula as we stated before, when we saw for our class midpoint for the first class, so we took 12 plus 18 divided by 2. And then following that pattern for the rest of our classes. So moving right along here. So now, using all the information we've collected together, we can put together our histogram. And I've gone ahead and and created a digital. Histogram for us to refer to. It's always important whenever you do any sort of histogram that you give it a title, which in this case it's employee overtime hours. Our Y axis or the vertical axis denotes our relative frequency, which is the proportion of employees, and our horizontal axis, the X axis, is our overtime hours. And then we have a little jagged line here that almost looks like a lightning bolt or a sideway Z and that shows a break in data points, so it skips over a bunch of data points and it starts at 15 to 22 to 29 to 46 to 53. Then we have our bars on our histogram which are represented in this beigey peach color. And they're all touching each other side by side, and that's what separates a histogram from a bar graph, because a histogram, all the bars are touching, whereas in a bar graph, the bars are separate and they don't touch each other. Awesome. So as you can see using our data points, we just plot our data as we discovered earlier and then we will produce the following graph. So for 15, we'll have a relative frequency of 0.20, and then for 22 we'll have a relative frequency of a little bit over 0.15. Etc. So all we're doing is we're just plotting. I said 0.20, but it's a little bit above it, technically for 15 overtime hours. And that's it. That is how you solve for this particular problem, and that is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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

c. Display the data using a relative frequency histogram.

Key Concepts

Relative Frequency

Histogram

Binning Data

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