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By: pyeo (offline)  Monday, December 28 2015 @ 07:24 AM CST (Read 934 times)  
pyeo

Help!!
1. In a diving competition, 5 judges each award a whole-number score from 1 to 10 and an average mark is then calculated. However there are 3 different ways of measuring the average: mean, mode and medium. After a particular set of scores were given, an argument arose as to which measure should be used, as this would lead to 3 different final marks being awarded: 7, 8 or 9. Work out all the different possible scores that could have been awarded. Which mark would match with each measure?

Thank you.

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By: nisalam (offline)  Tuesday, December 29 2015 @ 07:05 AM CST  
nisalam

If 9 is to be the mean, then neither 7 nor 8 can become the mode.
Similarly if 9 is the median, the marks will be x,y, 9, 10, 10 or x, y, 9, 9, 10 or x, y, 9, 9, 9 : all will mean neither 7 or 8 can be the mode.
Thus, 9 must be the mode: x, y, 8, 9, 9 and 8 the median.
That leaves 7 for the mean.
Total of 5 numbers= 35
So mark combinations can either be 2, 7, 8, 9, 9 or 3, 6, 8, 9, 9 or 4, 5, 8, 9, 9
Hope this helps.

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