Construct a frequency distribution for the data set using the ...

Question

Construct a frequency distribution for the data set using the indicated number of classes. In the table, include the midpoints, relative frequencies, and cumulative frequencies. Which class has the greatest class frequency and which has the least class frequency.

Textbook Spending

Number of classes: 6

Data set: Amounts (in dollars) spent on textbooks for a semester 91 472 279 249 530 376 188 341 266 199 142 273 189 130 489 266 248 101 375 486 190 398 188 269 43 30 127 354 84 319

Accepted Answer

Hello everyone. Let's take a look at this question together. A survey records the number of books read by 28 students during the summer, with the following values for that number of books read by the 28 students during the summer. In a frequency distribution using 5 classes, and include class midpoints, relative frequencies, and cumulative frequencies. So in order to solve, we have to recall how to construct a frequency distribution using 5 classes, as well as we need to include the class midpoint, sell frequencies, and the cumulative frequencies. And so the first step is to our data that we are provided, where we have our data, which is the number of books, and we organize the number of books read by the 28 students during the summer in ascending order. We know that our count is the 28 students. From our data, we know we have a minimum value of 1, and a maximum value of 5. Using the data, we can determine the class width, which we do so by first calculating the range, which is our maximum value subtracted by our minimum value, so 15 minus 1 is equal to 14, and plugging in the value. To find the class with, we have 14 divided by 5, which is 2.8, which when rounded, is equal to 3. So then we will use a class with equal to 3 and define the classes starting at 1. So then we define the class intervals, where we start with the minimum value, which is 1, add the class width, which is 3 successively, giving us the following class intervals of 1 to 34 to 67 to 9, 10 to 12, and 13 to 15. And then we can calculate. Points, which we know that the midpoint of each class is the average of its lower and upper bounds. Therefore, for the midpoint for the first class interval is equal to 1 + 3 divided by 2, giving us 2. Then for the class interval, we have 4 + 6 divided by 2, which is equal to 5, midpoint of the third class interval is 7 + 9 divided by 2, which is equal to 8. The fourth midpoint is 10 + 12 divided by, which is equal to 11. And lastly, the fifth midpoint is 13 plus 15 divided by 2, which is 14. So now we have all of the midpoints for each of the different classes, and now determine the count frequencies, where we count how many data points fall into each class, starting with the first class 1 through 3. We know that from our data, we have 5 students. Our second class, which is 4 through 6, we know that we have 6 students. Our third class, which is 7 through 9, we know we have 6. Our 4th class, which is 10 through 12, we know there are 5 students, and lastly, our 5th class, which is Through 15, we know there are 6 students. So these are the count frequencies for the 5 classes. And next we calculate the relative frequencies, which relative frequency is the proportion. Of data in each class, so it is calculated as the relative frequency is equal to the count frequency of our sample size, and for the first class, our relative frequency is calculated as 5, which is the count frequency of the first class divided by 28, which is our total count, so 5 divided by 28 is approximately. 1786. Then we calculate the relative frequency for the second class. Which is divided by 28, giving us approximately 0.2143, and our third class is also 6 divided by 28 is also approximately 0.2143, and our fourth class is 5 divided by 28, so it is approximately 0.086. And lastly, our fifth class is 6 divided by 28, giving us approximately 0.2143. So then we have the relative for all 5 classes. And now we can calculate our cumulative frequencies, which we know cumulative frequency is the running total of the free. So starting with our first class, the cumulative frequency is 5. Our second class cumulative frequency is calculated as 5 + 6, which is equal to 11. The cumulative frequency for our third class is calculated by 11 + 6, which is equal to 17. Our fourth class is calculated as 17 + 5 equals 22. And lastly, our fifth class is calculated as 22 + 6, which is equal to 28. So we have the cumulative activities for all 5 classes, which was the last calculation that we needed to create our frequency distribution table. So using all of the values that we have calculated, we have the following final frequency distribution table, including intervals, our midpoints, the frequency. the relative frequency, and the cumulative frequency for all 5 classes from our data. This is our final frequency distribution using 5 classes, which makes answer choice C the correct answer, and all choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Frequency Distribution

Midpoints

Cumulative Frequency

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