Using and Interpreting Concepts

Question

Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

Power Failures The durations (in minutes) of power failures at a residence in the last 10 years

18 26 45 75 125 80 33

40 44 49 89 80 96 125

12 61 31 63 103 28 19

Accepted Answer

Hello. In this video, we are told that a student recorded the number of pages read each day for 15 days. We want to find the mean, median, and mode of the data, and if any of the measures cannot be found or does not represent the center of the data, explain why. So, since we want to find the mean median mode of the data set, the first thing we want to do is we want to organize the data set from least to greatest. Doing so gives us the following data set. 12:15. 1515, 1818, 18. 212121. 24 27 Sorry, 24 27 27 And 30 Let me just fix that 24 real quick. OK, so here is the complete data set from least to greatest. So let's go ahead and start this problem by finding the mean of the data set. Now, the mean of the data set is going to be the sum of all the points given to us divided by the total amount of points. So, the sum of the entire data set is going to be 306. And we are going to divide this by the total amount of data that is given to us. Now, since the student recorded how many pages he read for 15 days total, that means that we have 15 pieces of data. So we are going to divide 306 by 15, and that is going to give us a mean of approximately 20.4. So we have a mean of 20.4. Next, let's go ahead and identify the median. Now, the median is the middlemost number of the data set. Since we have 15 pieces of data in total, the halfway or the middlemost value of the data set is going to be the 8th value. And that is going to be 21. So 21 is the 8th value in the data set, and that is going to be our median. Now, finally, let's go ahead and identify our mode. Now, the mode is the highest frequency of an individual number, or in other words, it's the number that pops up the most in the entire data set. But here, notice that we have 1518. And 21 that appear 3 times each. They are the highest repeating values in our data set, so since they all repeat the same amount of times, our mode is going to be the collection of all three of these values. So the mode is going to be 1518, and 21, and that is going to be the final part of the information that we are looking for. So just to recap, the mean is the sum that is averaged by the total amount of days, and that is 20.4. The median is the middlemost number in the data set, and that is 21, and the mode is the highest frequency of an individual number, and we have a three-way tie between 1518, and 21. And so with that being said, the solution to this problem is going to be B. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

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Key Concepts

Mean

Median

Mode

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