Question 253786: 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
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Model of the list of 7 numbers:
2..3,3...6.x..y....20
Why?
6 is the median so it is in the middle of the list.
There are 3 numbers to the left and 3 numbers to the right of 6
2 is to the left of 6 and 3 is the mode so there must be two 3's
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20 is to the right of 6 so there must be two numbers that are 7 to 19
and are not the same. Their average is between (7+8)/2 = 7.5 and
(18+19)/2 = 37/2 = 18.5.
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The average of the 2+3+3+6+20 = 34/5 is 6.8
Combining 6.8 with 7.5 gives an average of (14.3/2) = 7.15
Combining 6.8 with 18.5 gives an average of (25.3/2) = 12.65
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Question: Which of the following could be the average (arithmetic mean ) of the numbers in the list?
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Cheers,
Stan H.
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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
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