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.

Video Durations The lengths (in minutes) of seven educational videos from the Public Broadcasting Service (PBS) (Source: PBS)

83 67 90 55 56 119 52

Accepted Answer

Hello, in this video, we are asked to determine the mean, median and mode of the data set, if applicable. If any of these measures cannot be calculated or failed to accurately represent the data's central tendency, provide a brief explanation. So we're told that the duration of 7 educational podcast episodes from an online learning platform are 45, 38, 60, 52, 40, 75, and 39. Now, since we want to find the mean, median and mode of this data set, the first thing we want to do is we want to go ahead and order the data set from least to greatest. Reordering the data set allows us to rewrite the data set as the following. 38, 39. 40 4552 60 And 75. This is going to be the data set from least to greatest. Let's go ahead and start by solving for the mean. Now, in order to solve for the mean, we want to take the sum of all the values in our data set, and divide them by the total amount of values. The sum of all 7 episodes or all 7 data points is going to be 349, and since there are a total of 7 data points, we are going to divide this value by 7. So our mean is going to be defined as 349 divided by 7, and that is going to approximate to be 49.86. So this data set has a mean of 49.86. Now let's go ahead and find the median. Now, in order to find the median, we want to find the middlemost value of the data set. Since we are working with an odd numbered data set, specifically a data set of 7 values, the minimost value is going to be the 4th value, and that value is going to be 45. So this data set has a median of 45. Next, let's go ahead and find the mode. Now, the mode is the value that basically pops up more than once in the data set, or it's the value that has the highest frequency in the data set. Now, in this case here, every number pops up exactly once, which means that there are no repeating values in our data set. Since there are no repeating values, our mode, or at least this data set does not have a mode. So the mode is going to be none. And this is going to be the solutions to this problem, and the overall solution 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.

��app

Key Concepts

Mean

Median

Mode

Watch next