In Exercises 17–19, use the data set, which represents the poi...

Question

In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League)

8 8 8 6 0 73 26 1

0 5 58 1 7 5 10 63

0 5 10 0 31 5 15 45

16 29 10 73 5 3 0 65

Construct a frequency distribution for the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies.

Accepted Answer

Hello, everyone. Let's take a look at this question together. The data set below shows the weekly reading times in minutes of a sample of 30 people. Construct a frequency distribution for the data set using 5 classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. And here we have our data set of the weekly reading times in minutes of a sample of 30 people, and we need to construct a frequency distribution for the data set using 5 classes, and include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. And so the first step is to look at our data set of the values of the weekly reading times in minutes of the sample of 30 people, as well as the different components of the frequency distribution that we need to find, starting with the class limits, which is the smallest and largest values that can belong to each class, as well as the midpoints, which are the average of the upper and lower class limits, the Boundaries are the values that separate the classes without gaps between them. The frequencies are the number of data points that fall within each class. The relative frequencies are the proportion of the data points within each class, which is calculated by frequency divided by the total, and lastly, the cumulative frequencies are the sum of the frequencies for that class and all previous classes. And so the first step in solving this problem and creating our frequency distribution, is to calculate the range. which we know the range is calculated by taking the highest value and subtracting it by the lowest value. So looking at our data set, we know our range is calculated by 140, subtracted by 85, giving us a value of 55. And then using the value for the range, we can determine the class width. Which the class width is calculated by the range divided by the number of classes, and since the problem is asking us to create a frequency distribution using 5 classes, Our class width is calculated as 55 divided by 5, which is equal to 11. And so we have our class limits of 85 to 95, 96 to 106, 107 to 117, 118 to 128, and 129 to 139. And now we can calculate the midpoints for each of our 5 classes, which the midpoint is calculated by the upper class limit, subtracted by the lower class limit divided by 2, which, for example, for the first class of 85 to 95, our midpoint is calculated by 95, subtracted by 85 divided by 2, giving us our midpoint value of 90. For the first class, which we can then calculate the midpoint for the remaining 4 classes. And then after calculating the midpoint, we can then calculate the class boundaries for each of the following class limits, which the lower boundary is calculated as the lower limit, subtracted by 0.5. And the upper boundary is calculated by the upper limit plus 0.5. Therefore, for the first class, which is 85 through 95, the lower boundary is equal to 85 subtracted by 0.5, making the lower boundary for the first class equal to 84.5, and then the upper boundary is 95 plus 0.5, so it is 95.5. And we can calculate the class boundaries for the remaining 4 classes, and then using our data, we can create our frequency distribution with the calculated values, giving us the following table, which includes our class limits, our midpoints, the boundaries, the frequencies, the relative frequencies, and the cumulative frequencies. Therefore, the following table is our frequency distribution, which looking at our answer choices, we can identify that answer choice A is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Key Concepts

Frequency Distribution

Class Limits and Midpoints

Relative and Cumulative Frequencies

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