Question

The average of the 7 numbers 7, 9, 12, x, 5, 4, 11 is 9. The missing number is

• A. 8
• B. 10
• C. 13
• D. 15

Hint:

To solve missing-number average problems, quickly multiply the given average by the total count of numbers to find the target sum, then subtract the sum of the known values.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The average (arithmetic mean) of a set of numbers is calculated by dividing the sum of the numbers by the count of those numbers.
Key Formula or Approach:
The formula for the mean of $n$ observations is:
\[ \text{Mean} = \frac{\sum x_i}{n} \]

Step 2: Detailed Explanation:
We are given:
Dataset: $\{7, 9, 12, x, 5, 4, 11\}$
Number of observations, $n = 7$
Average of the observations = 9
First, find the sum of the known numbers:
\[ 7 + 9 + 12 + 5 + 4 + 11 = 48 \]
Therefore, the sum of all 7 numbers is $48 + x$.
Set up the equation using the mean formula:
\[ \frac{48 + x}{7} = 9 \]
Multiply both sides of the equation by 7:
\[ 48 + x = 63 \]
Solve for the missing value $x$:
\[ x = 63 - 48 = 15 \]
The missing number is 15.

Step 3: Final Answer
The correct option is (D).