Construct a cumulative frequency distribution and an ogive for...

Question

Construct a cumulative frequency distribution and an ogive for the data set using six classes. Then describe the location of the greatest increase in frequency.

Retirement Ages

Data set: Retirement ages of 35 English professors 72 62 55 61 53 62 65 66 69 55 66 63 67 69 55 65 67 57 67 68 73 75 65 54 71 57 52 58 58 71 72 67 63 65 61

Accepted Answer

Hello, everyone. Let's take a look at this question together. Construct a cumulative frequency distribution for the given data using 6 classes. The following are the ages at which 36 high school teachers retired. And here we have the data value that we need to create our a cumulative frequency distribution for using 6 classes. And we also want to know where does the greatest increase in cumulative frequency occur? So, in order to solve this question, we have to recall how to construct a cumulative frequency distribution so that we can construct one for our given data of the ages at which 36 high school teachers are required using 6 classes, and then we want to know where does the greatest increase in cumulative frequency occur. And we know that the first step in solving this problem is finding the range of the data, which from our data set, we know the lowest age is 50 and the highest age is 89. Therefore, our range is calculated as 89 subtracted by 50, which is equal to 39. And using the range, we can determine the class width. Where we divide the range by the number of classes. So our class width is equal to 39 divided by 6, which is approximately 7, and then using the class width, we can set up the class intervals where we start at 50 and add the class width of 7 to each lower class limit, giving us the following class intervals. And now we can tally the frequencies for each class. Where we count the number of data points in each class, starting with the first class of 50 through 56, which contains the following data points. So the first class has 4 data points, and then we tally the frequencies for the remaining classes where we can see the number of data points that are in each class interval. And using this data, we can then construct the cumulative frequency distribution table. Where we add each class frequency to the sum of the previous frequencies. Which results in the following cumulative frequency distribution of the retirement ages of the high school teachers, where we have our class intervals, their frequency, and then the cumulative frequency. And then we need to identify where the greatest increase in cumulative frequency occurs. Which, looking at our cumulative frequency distribution, we know the greatest increase is 7, which occurs between the classes 64 through 70, 71 through 77, and 78 through 84. Therefore, the following cumulative frequency distribution of the retirement ages of the high school teachers is the correct frequency distribution. And the greatest increase in cumulative frequency, which is 7, occurs in 3 class intervals. So, answer choice C is the correct answer. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Cumulative Frequency Distribution

Ogive

Class Intervals

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