+24 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
+129899
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
