SOLUTION: The least and greatest numbers in a list of 7 real numbers are 2 and 20 ,respectively. The median of the list is 6 , and the number 3 occurs most often in the list. which of

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Question 363475: The least and greatest numbers in a list of 7 real numbers are 2 and 20 ,respectively. The median of the list is 6 , and the number 3 occurs most often
in the list.
which of the following could be the average (arithmetic mean) of the numbers in the list ?
I 7
II 8.5
III 10
(A) I only
(B)I and II only
(c) I and III only
(D) II and III only
(E) I, II, and III
Answer by robertb(5830) About Me  (Show Source):
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(E) I, II, and III.
We could have the following arrangement for the numbers:
2,3,3,6,x,y,20, in ascending order. The mean is formed as follows:
%282%2B3%2B3%2B6%2Bx%2By%2B20%29%2F7++=+%2834%2Bx%2By%29%2F7.
If the average is 7, then x+y = 15, which is very much possible for two numbers x and y between 6 and 20.(Take 7 and 8, e.g.) If the average is 8.5, then x+y = 25.5, which again is possible for two numbers between 6 and 20 (take 10 and 15.5, e.g.) If the average is 10, then x+y = 36, which again is possible for two numbers between 6 and 20 (take 17 and 19, e.g.)