Large Data Sets from Appendix B. In Exercises 25–28, refer to ...

Question

Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.

Weights Use the weights of the males listed in Data Set 2 “ANSUR I 1988,” which were measured in 1988 and use the weights of the males listed in Data Set 3 “ANSUR II 2012,” which were measured in 2012. Does it appear that males have become heavier?

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says use the following recorded weights in kilograms of a group of individuals measured in 2 different years. Find the mean and median of each set of data, and then compare the two sets of results. How have the weights changed over time? And here we're given a table that has two columns. In the first column, we have year 1, and it has values of 72, 75, 78, 70, 74, 77, 73, and 76. And for the second column, is labeled year 2, and it has the values of 80, 85, 82, 79, 84, 83, 81, and 86. We're also given 4 possible choices as our answers. For choice A, the medians indicate that individuals in year 1 weigh more than those in year 2. For choice B, the weights in year 2 are higher than in year 1 as indicated by both mean and median. For choice C, the weights in year 1 are higher than in year 2, based on the mean, but not the median. And for choice D, the means suggests that weights have remained the same over time. So, the first part of this problem, we need to calculate both the means and the medians. So we're gonna start off by calculating the means. And so, we call for the mean, which is going to be X bar. That is going to be equal to the sum. Of X I divided by N, where X of I is an individual data point and N is the number of data points. So we're gonna do this for both year one and year 2. So, for X bar 1, which is going to be the mean for year 1, this is going to be equal 2. The quantity of 72 plus 75. Plus 78. Plus 70 Plus 74. Plus 77. Plus 73. Plus 76. And in quantity, and all of that it's going to be divided by the number of data points that we have. Which is 8. And when we evaluate this expression, this is going to be equal to. 74.38. Kilograms, and here we just rounded to two decimal places. That would do the same thing for year 2, so that'll be X bar 2. And that's gonna be equal to, and here we'll add up all the data points in the numerators, so we'll have the quantity of 80. Plus 85. Plus 82. Plus 79. Plus 84. Plus 83. Plus 81. Plus 86 in quantity, and all of that is divided by the number of data points, which again is 8. And when we evaluate this expression, this is going to be equal to 82.5 kg. So now we've calculated both the means, we need to calculate the medians. So, for the medians, we'll first want to arrange our data in ascending order. So we'll start from the lowest value and go to the largest value. So, for year one, when we order our data, we're going to have 70 In 72. 73 In 74. In 75 Then 76 In 77 And then 78. And then 4. Year 2, we're going to have 79. 80? 81. Then 82 Then 83. Then 84. Then 85 In '86. So, now that we have our data ordered, we just need to find the median, which is going to be the value in the middle. And since we have An even number of data points, 8. We're actually going to look at the value that is in between the middle two data points. So, for year one, The median for year one, which we call median one. is going to be equal to the midpoint between 74 and 75. So, to calculate that, we'll add those two values together, so we'll have the quantity of 74 plus 75 in quantity and divided by 2. And doing so, this is going to be equal to. 74.5 kg. Now, we did the same thing for year 2, and so the median. For year 2, which we'll call median 2, is going to be equal to, and again, we'll take the middle two values. And find the midpoint between those. So the mil two values of our data set are going to be 82 and 83. We'll have the quantity of 82 plus 83 in quantity, divided by 2, which is going to be equal to 82.5 kg. So now that we have calculated both the mean and median, we need to compare the results for the 2 years. Now, if you look at the mean and median for year 1, we see that they're very close, and this would indicate a balanced distribution. And if you look at the mean and medium for year 2, they're exactly the same, which would indicate a symmetrical distribution. Now, since both of the mean and median for year 2 are higher than those of year 1, it appears that individuals have become heavier over time. So that means that the correct answer for this question is answer choice B. The weights in year 2 are higher than in year 1, as indicated by both the mean and median. So, I hope that this explanation has been useful, and I'll see you in the next video.

��app

Key Concepts

Mean

Median

Comparative Analysis

Watch next