More Than One Mode?
Date: 10/07/2002 at 17:02:08 From: Robin Redsull Subject: Statistical mode Dr Math - I teach one section of statistics to advanced math students and we came upon an answer we did not agree with. We would like your help in determining if the answer is a misprint. And if it is not a misprint, we would like an explanation for the answer! By definition, a statistical mode is the value(s) that occur most frequently in the data set. What is the mode of the data set: 13, 13, 14, 14, 15, 15? We say 'none' because no number appears more frequently than any other number. The answer key said 13, 14 and 15. What do you say?? Thank you - Robin Redsull
Date: 10/07/2002 at 17:59:54 From: Doctor Achilles Subject: Re: Statistical mode Hi Robin, Thanks for writing to Dr. Math. The other day, I was running a race against two other people. The other two people finished ahead of me, but at EXACTLY the same time. So they BOTH got first place and I got third place (there was no second place). By definition, the winner of a race is (are) the runner(s) who finish with the fastest time. If two runners tie for first, they both win. If three, four, or more runners all get the EXACT same time, then they all win. So the way to decide the winner of the race is to give each runner a time, like this: Runner A: 1min23sec Runner B: 1min25sec Runner C: 1min23sec The winner(s) is (are) the runner(s) who has (have) the fastest time. To figure that out, we find the fastest time: 1min23sec So EVERY runner with a time of 1min23sec is a winner. In the data set: 1, 1, 1, 2, 2, 2, 3 1 and 2 both have the most occurrences, so they are both modes. Since they tie for first place, they both get it. 3 is not a mode because it occurs less frequently. So the way to find a mode is to give each number a score based on how many times it occurs. 1: occurs three times 2: occurs three times 3: occurs one time The mode(s) is (are) the value(s) that occur(s) the most. The most any value appears is: three times So every number that occurs three times is a mode. Hope this helps. If you have other questions about this or you're still stuck, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
Date: 10/08/2002 at 12:22:50 From: Robin Redsull Subject: Statistical mode Dr Math - Thanks for the quick reply to my question. I totally agree with your comments and completely understand them. But you didn't really address my question. If your data set is: 13, 13, 14, 14, 15, 15, is there a mode, and what is it? Robin Redsull
Date: 10/08/2002 at 14:16:35 From: Doctor Achilles Subject: Re: Statistical mode Hi Robin, Thanks for writing back to Dr. Math. In that data set, the modes are: 13, 14, and 15. In the data set: 1, 13, 13, 14, 14, 15, 15 The modes are also: 13, 14, and 15. You can have multiple modes in a data set. Hope this helps. If you'd like to talk about this some more, please write back. - Doctor Achilles, The Math Forum http://mathforum.org/dr.math/
Date: 10/08/2002 at 12:30:08 From: Doctor Sarah Subject: Re: Statistical mode Hi Robin - thanks for writing to Dr. Math. When no number occurs more than once in a data set, there is no mode. If each of two numbers occurs twice, we say the set is bimodal. Your set is trimodal. See: Statistics - edHelper.com http://www.edhelper.com/statistics.htm Mean, Median, and Mode Discussion - Shodor Education Foundation http://www.shodor.org/interactivate/discussions/sd1.html - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/
Date: 10/08/2002 at 12:35:51 From: Robin Redsull Subject: Thank you (Statistical mode) Thank you for your answer! What a neat resource to have access to. Now that I have found it - I'm sure my students will take advantage of it and try to come up with interesting questions to try to stump you all.
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