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.

Weights (in pounds) of Packages on a Delivery Truck

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Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says the following stem and leaf plot shows the ages and years of participants in a community workshop. Find the mean, median, and mode of the data, if possible. If any measurement cannot be found or does not represent the center of the data, explain why. And below, the texts were given a stimulle plot. So, in the first row, we have a stem of 0, and it only has one leaf of 9. In the next row, we have a stem of 1, and it has 4 leaves of 257, and 9. The next row, we have a stem of 2, and the leaves of 02558, and 9. For the next row, we have a stem of 3, with the leaves of 11, 3446 and 7. The next row we have a stem of 4, and the leaves of 02257, and 8. And for the last row, we have a stem of 5, with only 1 leaf of 1, and we're given the key that a stem of 2 and a leaf of 0 is going to be equal to 20. So in this problem we're asked to find the mean, median and mode of our data. So the first thing we need to do is to convert our similar leaf plot into actual data. So, using our key in the first row, we'll just have the value of 9. In the next row, we will have the values of 12. 15 17 and 19. In the next row will have the values of 20. 22. 25 25 28 And 29. In the next row we'll have the values of 31. 31 again. 33 34. 34 again 36. And 37. In the next row will have the values of 40. 42. 42 again. 45 47 And 48. And in the final row, we'll just have the value of 51. So now that we have all of our data values, we can calculate the mean. And recall that the mean is going to be equal to the sum of all of our data values divided by the number of data values that we have. So in the numerator, we'll have the quantity of 9 + 12 + 15. Plus 17 + 19. Plus 20 + 22 + 25. Plus 25. Plus 28 + 29. Plus 31, + 31. Plus 33. Plus 34. Plus 34. Plus 36. Plus 37. Plus 40. Plus 42 + 42. Plus 45. Plus 47 + 48, and plus 51. That whole quantity is divided by the number of data points that we have, and we count up all the data points, we see that we have 25 data points. So we'll divide this whole quantity by 25. And so simplify this expression, this is going to be equal to. 772 divided by 25. Which is going to be equal to. 30.88. So that is the value of the mean that we were looking for. Next quantity that we want to calculate is going to be the median. Recall that the median is going to be the value that appears in the middle of our data set, once we have ordered our data. And here we already have our data ordered in ascending order, starting with the lowest value at the top. And going to the largest value from the bottom. And since we have 25 data points, the value that is going to show up in the middle is going to be the 13th value in our sequence here. And when we look at the 13th value, that turns out to be 31. That means that our median is going to be equal to 31. And so that is the 2nd quantity that we're actually looking for. Now, the last quantity that we need to find is going to be the mode. I recall that the mode is the value or values. That occur with the highest frequency. And if you look at our data set here, we see that we have 4 values that occur twice. So, we have 25. 31 34 And 42. And so, since those are the values that occur with the highest frequency, those are going to be our modes. So for a mode, we're gonna have 25 31 34 and 42. That is the values that we're looking for for the last quantity, which is our mode. So just to recap, we have a mean of 30.88, a median of 31, and a mode of 25, 31, 34, and 42. So those are the answers that we're looking for for this problem. So I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Mean

Median

Mode

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