Descriptive statistics problem

[TheGmatTutor]

A list of 7 numbers consists of the integers n, 3, 14, 8, 10, 12, and 4. If the median of the list is equal to the mean, what is the value of n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Answer: C

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Hi TheGmatTutor,

This question can be solved in a couple of different ways; it would probably help a great deal to pay attention to the answer choices though.

The given numbers in the set of 7 are....3, 4, 8, 10, 12, 14.....and N. Since the answers are relatively small --> 3, 4, 5, 6 and 8, once that additional value (N) is included in the set, the MEDIAN WILL = 8.

Since we're told that the MEAN of the set = the MEDIAN of the set, we know that the MEAN = 8.

Thus, (3+4+8+10+12+14+N)/7 = 8.....

3+4+8+10+12+14+N = 56
51 + N = 56
N = 5

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

A list of 7 numbers consists of the integers n, 3, 14, 8, 10, 12, and 4. If the median of the list is equal to the mean, what is the value of n?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

The median of the list is equal to the mean.
Since the list contains an ODD NUMBER OF INTEGERS, the median -- and thus the mean -- is equal to an integer value.

Sum = (number of integers)(mean).
Sum of all 7 integers = (7)(mean) = (7)(integer value) = multiple of 7.
Sum of the 6 known integers = 3+4+8+10+12+14 = 51.

Since the sum of the 6 known integers = 51, and the sum of all 7 integers must be a multiple of 7, the correct answer choice must yield a multiple of 7 when added to 51.
Only C works:
5 + 51 = 56 = multiple of 7.

The correct answer is C.