10, 11, 13, 13, 15, 19, 22, 23
Mean
All data points are added together, and their sum is divided by the total number of data points. The mean is also commonly referred to as the "average," and is used with numerical data.
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It is best to use the mean when there are no outliers, or data points that are far away from the other data (an example would be the number 50 using the above numbers). An example of when the mean would be the best representation of the data is a sprint race. A sprint race is a short footrace that is usually less than a quarter of a mile run at top speed. Generally, you would expect that all finish times are around the same time. So, if you were trying to determine an "average" of how long it took each runner to run the race, the mean would be a good way to determine it.
Median
The median splits the data points exactly in half, and is used with numerical data. If the data points are not already in ascending order, this must be done first before you can proceed. The easiest way to determine the median, is to cross off a data point from each end until you have one data point remaining in the center. If there are an odd number of data points, this is easy to do. However, if you have an even number of data points as I do in my data set, you will actually end up with two data points left in the center. In this case, you will need to find the mean of the two remaining data points in order to determine the median.
Median
The median splits the data points exactly in half, and is used with numerical data. If the data points are not already in ascending order, this must be done first before you can proceed. The easiest way to determine the median, is to cross off a data point from each end until you have one data point remaining in the center. If there are an odd number of data points, this is easy to do. However, if you have an even number of data points as I do in my data set, you will actually end up with two data points left in the center. In this case, you will need to find the mean of the two remaining data points in order to determine the median.
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It is best to use the median when there are outliers present, as they should not affect the outcome. An example of when the median would be the best representation of the data is with test scores. You may have some zeros for those who did not take the test, and you may have some that scored a high "A." However, to obtain a better idea of how the class performed overall, you would not want these outliers taken into account. Therefore, the median may be the best fit here.
Mode
The data point(s) that occurs most frequently in the set, and is used with both numerical and categorical data. There may be no mode, two modes (bimodal), three modes (trimodal), or greater than three modes (multimodal). Generally, however, more than two modes is uncommon.
It is best to use the mode when you are looking for the most popular result. An example of when the mode would be the best representation of the data is when determining favorite kind of pizza using a bar graph (categorical data). You will be able to determine the mode simply by locating whichever bar is the largest.
Still confused?
I hope that this post helped clarify some of the muddy points for you. If not, I found this short video on Khan Academy's website that does a great job explaining what each measure represents. Perhaps hearing and seeing it worked out will help.
Mode
The data point(s) that occurs most frequently in the set, and is used with both numerical and categorical data. There may be no mode, two modes (bimodal), three modes (trimodal), or greater than three modes (multimodal). Generally, however, more than two modes is uncommon.
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| Work by me |
It is best to use the mode when you are looking for the most popular result. An example of when the mode would be the best representation of the data is when determining favorite kind of pizza using a bar graph (categorical data). You will be able to determine the mode simply by locating whichever bar is the largest.
Still confused?
I hope that this post helped clarify some of the muddy points for you. If not, I found this short video on Khan Academy's website that does a great job explaining what each measure represents. Perhaps hearing and seeing it worked out will help.
Tools for Teachers
I found some great sites that would be helpful in teaching measures of central tendency:
I found some great sites that would be helpful in teaching measures of central tendency:
- Illuminations, which I have mentioned in previous posts, is an excellent tool for teachers. This link in particular brings you to a search I did on the site for mean, median, and mode. There are several lesson plans provided, which include grade level appropriateness and activity sheets.
- education.com is another site I found that provides lessons, worksheets, and etcetera. This link in particular brings you to a fun card game I found on the site for helping students master measures of central tendency. Plus, cards are a cheap manipulative you can also use in your probability lessons.
- Math Worksheets 4 Kids is a site that is just what its name says, math worksheets for kids! This link in particular brings you to central tendency worksheets. Different levels are provided, worksheets for each individual topic, and worksheets for multiple topics on one are also provided. What I liked most, is that they provide the answer key for you!
Hopefully, you will now be able to distinguish what the measures of central tendency are, and when best to use them.
-Amanda
-Amanda
After reading this post, I am so upset that I did not read this the day before the test. Measure of central tendency is the one subject that I struggled with on the test. I now know how to explain when would be the best appropriate time to use each one when as before I was so lost. Thank you for clearing this up for me. You did an absolutely wonderful job of explaining each one in great detail. I for one hope you keep doing this math blog even though our assignment is over. I have really benefitted from it and you have really helped me with some of my "fuzziness". You are going to be an excellent teacher!
ReplyDeleteThank you, Samantha! Receiving that kind of compliment means a lot coming from a fellow future educator!
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