Nicotine in Cigarettes Some of the nonparametric methods in th...

Question

Nicotine in Cigarettes Some of the nonparametric methods in this chapter use ranks of data. Find the ranks corresponding to the following amounts (milligrams) of nicotine in king-sized cigarettes (from Data Set 16 “Cigarette Contents” in Appendix B).

1.1 1.7 1.7 1.1 1.4 1.0 1.2 1.8 1.6 1.1

1.1 1.7 1.7 1.1 1.4 1.0 1.2 1.8 1.6 1.1

Accepted Answer

Welcome back, everyone. Listed below are the scores out of 100 achieved by a group of students in a math exam. Find the ranks corresponding to these scores. We're given 7885, 85, 72, 80, 75, 77, 88, 82, and 79. So if we want to assign ranks, what we first will have to do is arrange our scores from highest to lowest. So the highest one is 88. Which is followed by 85 and 85 again, we're going to include 85 2 times. Followed by 82. The next one is going to be 80. Which is followed by. 79, 78, 77, so 79, 78, 77, and then we have 75 and 72. So now we're going to rank them as follows, starting with the highest one, it gets ranked number one. Followed by 85, which gets ranked number 2. Now, since the third one is 85 again, we cannot assign rank number 3, right, because it's the same value as the previous one. So essentially it tells us that the second and the third values they are going to share the same rank, meaning the second value is not going to have rank number 2. What we have to do is basically understand that 85 and another 85 would technically share ranks 2 and 3. So what we have to do is basically identify the average of those ranks. So we're going to add 2 and 3. And divide that by 2.5 divided by 2 gives us a rank of 2.5, which essentially means that the values of 85 will correspond to rank 2.5. Meaning 88 gets rank 1, 85 gets rank. 2.5, another 85 guests. Rank 2.5 again and because 3 was part of the average, the next value of 82 immediately gets rank 4. So we're skipping the ranks. We arrived because it was part of the average and then 80. Gets a lower rank that would be 5. Followed by 79. That would be rank 6. 78 Rank 7 as we can see, there is no repetition, so we don't need to average out, right? 77, that would be the next one, rank 8. 75. Rank 9. And 72. Would be the final one, rank 10th. And that's it. We have our final ranks. Let's label them and thank you for watching.