The mean, the median, the mode of the distribution of the heights of 9 boys from the school basketball team are all equal to 183cm. three of the boys have a height of 183cm and the tallest boy has a height of 187cm. given that the heights of all the boys are integers, find the least possible height of shortest boy


the answer is 172


give me the working

 May 18, 2017
edited by bennykim0905  May 18, 2017


Note that we can have the following distribution of heights :


a b  183  183  183  c d e 187


Note that  if all nine boys  averaged 183 cm, the total number of cm  =  1647 


But.....we know that one boy has a height of 187 cm  and three of them have a height of 183 cm...so...


187  + 3 (183)  =  736 cm


So.....the remaining number of cm to be allotted amongst the other five boys is 1647 - 736  = 911 cm


Now.......assume that boys   "d" and "e" can be 186 cm tall,  boy "c" can be 185 cm tall  and boy "b" can be 182 cm tall......these are the max heights possible under the given constraints and will guaratnee the shortest boy possible...then....the shortest boy "a"  is


911  - 2(186) - 185 - 182  =  172  cm tall


And the heights  are


172  182 183 183 183 185 186 186 187


Check to see that the mean, median and mode  = 183




cool cool cool

 May 18, 2017
edited by CPhill  May 18, 2017

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