If the average of numbers: 4,7,5,6,8,n,4 is equal to their median, which of the following could be the value of n?

Answer 1

Average of these number is the sum of them divided by the count (there are seven numbers):

(4+7+5+6+8+n+4)/7 = (34+n) / 7

Median is the mid point of the ordered series. So, first order the numbers:

4 4 5 6 7 8 . We do not know where n may be. Let;s see possible median values:

1) If n is in the first half of the series, [n 4 4 5 6 7 8] or [4 n 4 5 6 7 8] or [4 4 n 5 6 7 8], the median is 5. Then

5 = (34+n)/7 (multiple both sides by 7)

35 = 34 + n => n = 1. This is definitely possible since it means n is the first in the series, which is in the first half. SO, this is a possible solution

2) If n is in the second half of the series, [4 4 5 6 7 8 n] or [4 4 5 6 7 n 8] or [4 4 5 6 n 7 8], the median is 6. Then

6 = (34+n)/7 (multiple both sides by 7)

42 = 34 + n => n = 8. This is definitely possible since it means n is the last in the series, which is in the second half. SO, this is a possible solution

3) n is the median [4 4 5 n 6 7 8], which means n is in the region [5 6]. n = (34 + n) /7 => 7n = 34 + n => 6n = 34 => n = 34/6 = 5.66666. So, this is a possible answer too.