Question

100 POINTS!!!! The median of the set of numbers 12, 38, 45, $x$, 14 is five less than the mean. If x is a negative integer, what is the value of x?

Answer 1

-14

Explanation:

Since x is negative, the median of the set is 14. Therefore, the mean of the set is 14 + 5 = 19, and its sum is 19 · 5 = 95. Since 12, 38, 45, and 14 sum to 109, the remaining integer x must be 95 − 109 = −14 .

Answer 2

• x = -14

Explanation:

Given set of numbers:

• 12, 38, 45, x, 14

Put them in ascending order, considering the x is negative

• x, 12, 14, 38, 45

The median is 14

The mean is 5 greater than median:

• 14 + 5 = 19

The mean is calculated:

• (x + 12 +14 + 38 + 45)/ 5 = 19
• x + 109 = 19*5
• x = 95 - 109
• x = -14