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.

College Credits The number of credits being taken by a sample of 14 full-time college students for a semester

12 14 16 15 13 14 15

18 16 16 12 16 15 17

Accepted Answer

Hello, in this video, we wanted to determine the mean, median and mode for the given data set, and then we want to provide a brief explanation if any measure is not applicable or does not accurately reflect the central tendency. So we are told that the daily screen time and hours is recorded for a sample of 14 high school students. So, the first thing we want to do is you want to organize this data set from least to greatest. Organizing the data set from least to greatest gives us the following. We have 4, 4.5, 55, 5.5, 5.5, 666, and 6. 6.5. 7 and 7.5. OK, so this is going to be the data set from least to greatest. Now, the first thing we want to do is we want to go ahead and find the mean of the data set. Now, in order to find the meaning of the data set, we want to take the sum of all the values in our data set and divide it by the total amount of values we have. So the sum of all 14 pieces of the data given to us is going to be 79.5, and we will divide this by the total amount of data that we have. Now, again, we are told that the daily screen times recorded was given for 14 high school students. So we have 14 pieces of data in total, therefore, we are dividing our sum by 14, and this is going to give us a mean of approximately 5.68. So that is going to be the mean of our data set. Now let's go ahead and find the median. Now, the median is the middlemost value of our data set, but we are working with an even value data set, which is 14. So, what we are going to do is we are going to pick the two middlemost numbers of our data set and average them. The 2 minimal numbers of a data set of 14 is going to be the 7th and 8th piece of data. So, the 7th piece will be 6 And The minimal values are going to be 5.5 and 6. So, if we take the sum of these two values, that is going to give us 5.5. Plus 6, and we're going to average that to 2. 5.5 + 6 is going to give us 11.5. And we will divide that by 2, and that is going to give us a median of 5.75. So that is the median of the data set. Finally, we are going to identify our mode. Now, the mode is the highest frequency of an individual number, or in other words, we are looking for the number that pops up the most in our data set. Well, that number is going to be 6, because it appears 4 times, which is the highest frequency compared to all the other numbers in our data set. So our mode is going to be 6. And so to recap, we have a mean of 5.68, a median of 5.75, and a mode of 6. And with that being said, the solution to this problem is going to be D. 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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